A brief rundown of the three basic parts of NDN law

Tribal sovereignty and NDN property rights
Obviously, before the settlers came to what is now the United States, the tribes ruled themselves and lived as they saw fit to live. But once the settlers came, things changed.
The settlers realized pretty quickly that they had 2 options - they could fight the indians, or they could try to work with the indians in order to settle in the area. In the earliest days, the settlers were just shiploads of people, and they realized they had enough on their plates just trying to survive without having to worry about a bunch of pissed-off indians. So a lot of the earliest dealings with the indians involved making deals with the indians... about who could live where and so on.
Part of the settlers' mindset was that it was their god-given duty to teach these indians about god, and to "tame" or to "civilize" them. As such, they did not view the indians as equals, but, often, as savages. The settlers sort of felt that they had "discovered" the new world because they were the first "civilized" people to reach these shores, and so they just plain didn't see that the indians had been "discovering" this land for thousands of years before them.
But they couldn't see them as total savages. In order to make peaceful agreements with the indians, they had to at least recognize them as "sovereigns" - and they had to negotiate with their representatives.
Because to their way of thinking, if they didn't treat the indians as capable of negotiating and treatymaking, then any agreements they made with the indians were not going to be recognized as valid.
You can't say "but they gave this land to us" if you don't recognize them as having that power, right?
Anyhow, following the methods of colonization, once they had acquired title or possession of land from the Indians, they saw this title of land as "good against the claims of other European Powers." See, it wasn't just one group of people out there trying to colonize and claim America, it was many. Several European countries were all in competition to explore and discover and claim new lands - and according to protocol in Europe, if the English settlers made a treaty with a tribe that gave them land, the Spanish couldn't come in and make a deal with the indians for that same land because the English already had it.
In this way, the different groups of people coming over for Europe were able to make some pretty big land grabs, in part by offering to protect the indians from the OTHER groups of colonizers that were coming over, from other countries.
We'll get into the history more later, but let's suffice to say that by the time the dust settled and the English had claimed most of the US, and then the US had then declared itself independent of Britain and become it's own nation, treatymaking was a fairly commonly used tool to make deals with the indians, and they were respected as having the power to make treaties.
But just because they had the power to make treaties giving land to the settlers in exchange for peace and money and protection and goods, didn't mean they had the full "title" to the land. Instead, the colonists viewed them as having a "right of occupancy" - since they were, after all, to the settler's way of thinking... "savages" and therefore not equal human beings. The settlers figured that since they had "discovered" America, THEY held the real ownership of the land, but that the treaties were a great tool for getting the Indians to help them peacefully get control over it.
At any rate, by the time we adopted the Constitution, treaties were pretty common. And now, the relationship of the indians to the government is not seen as equal governments with equal powers to make agreements, but rather, the US sees that tribes are "dependent domestic nations" - meaning they rely on the US for protection.
And the US used these treaties to move the indians, a little bit at a time, out of lands they wanted to settle, and as they would create and re-negotiate new treaties, they would end up with the indians giving more and more of their land up, and would push the indians further and further out west so the settlers could settle the Eastern part of the US.
But the problem with this was... as soon as the east was settled, the colonists realized they wanted the west, too. A lot of shuffling was done, and a lot of reservations were created,and a lot of warring happened while all this was going on. But one of the main ways by which the government was able to make the indians move was by agreeing in treaties to give them certain areas of land (and sometimes they offered protection and money and food and other things) in exchange for their giving up other chunks of land.
The US still respects the treaties, generally, that were created during the early years. The treaties promising lands to the indians "in perpetuity" are still enforceable, and the US still respects some sovereign rights of the indians. Part of the agreements made back then was that indians could still retain control of their tribes, and could still rule them as they wanted. And to some extent, those powers remain in force today, although subject to certain limitations. And the federal government still sees themselves as having the ultimate control over the WHOLE US, meaning that they have "plenary" or complete power to change or get rid of the treaties or to do whatever they choose with the indians.
Still, the rights the Indians have kept can be important, as you will see later. They retained a lot of hunting and fishing rights - both on and off the reservations, and they have kept special water rights, which can be important in the western states where water is hard to come by. And Congress has generally respected their rights to rule their separate nations within the US borders. This rule of self-government is important and will come up a lot later.

Federal Power and Obligations
These agreements with tribes, and the treaties, and 200 years of special legislation for the indians has created a very unique relationship between the Indians and the US government.
For starters, the federal government pre-empts states when it comes to control of the tribes. They don't deal with the states so much, they have to come to the feds. Also, the government realizes that because of their history, they have a special obligation to treat the indians right, and to take care of them.
One of the first things the US government did was pass a Trade and Intercourse Act - what this did was protect, in some ways, Indian land. The Act said that the feds had to be a participant in any trade or sale of indian land - meaning they had to give their approval. This may seem a little controlling, but if you think about it, there were a lot of shady settlers back in the 1700s and 1800s who would go out and try to trick or cheat the indians out of lands the government had promised them. And if the indians fell on hard times, they might have felt forced to give up some of the land that was still "theirs" in order to get food or supplies for survival. So with this new rule in place, indian land was protected from sketchy pioneers who wanted to try to outsmart the indians and get their land for a good deal. With the government requiring that they give approval for land sales and trades, they could make sure that everything was on the up-and-up. And if someone DID go in and buy indian land, the government could invalidate that agreement, so the purchaser ended up with nothing, and the land was given back to the indians.

The government has also recognized it's obligations to the indians in other ways, through special programs. Lots of these programs relate to protecting and developing NDN lands, assisting the tribal governments, and in creating special assistance programs to address educational and health needs of indians. And indians are one of the very few groups that can end-run certain equal-rights provisions of the US Constitution and actually have hiring preferences for indians in the BIA and Indian Health services - in most other areas, specifically preferring to hire someone based on their race is illegal. The government sees these special obligations to the indians as just part of fulfilling this "special trust relationship" between the indians and the federal government.

Keep in mind, though, that Congress still has reserved the right to ultimate power over indians. And Congress has reserved the right to abrogate, or cancel, treaties at any time, with or without the consent of the indians. They can kill the indian title to the land, and they can even end the "special relationship" they currently recognize as existing between indians and the feds. They probably won't, because they have been pretty good about showing respect over the history of the country in regards to their obligations, and because that would be a political nightmare for everyone involved, but they DO reserve that right over all. The extent of their power is only checked by the second arm of the government - the US supreme court, which has said it will review any actions that congress takes that challenge the indian's rights to land or self government or anything else for that matter.

Jurisdiction over the rez
This is the third big issue/area of indian law. Under the tenth amendment to the constitution, states have police power, but this is really scaled back in indian country. The feds exclude most state jurisdiction on the reservations, and let the indians deal directly with them.
As such, most state laws that deal with things like zoning, the environment, domestic issues and child welfare, don't extend to indians in indian country.
Don't let this fool you, though. Sometimes, states don't just accept this assertion of tribal immunity, and a lot of the case law we'll get into later deals with the states trying to assert power in a reservation.
But this area of indian law is a hotly debated one. Federal courts have held that certain rights reserved to the NDNs in treaties, such as the right to harvest up to 50% of the salmon and steelhead in some of the nations largest fisheries, even if they are not part of the reservation, are still intact. And there are issues with off-reservation fishing and hunting rights that still exist today because they were promised in a treaty. And of course, there are the state taxation laws... these cause lots of issues between states and reservations.
The bottom line is... because of the three different sets of laws - federal law, state law and tribal law, it can get confusing to try and figure out who has the authority to make or enforce laws on and off the rez, for indians and non-indians alike. Sometimes, jurisdiction over someone who commits a crime depends on whether they are indian or non, and whether they were on or off the rez when it happened. In some cases, courts have even held that where tribal interests are not affected, state laws CAN be enforced in indian country.
So we'll get more into that later. But these three areas of NDN law are the main ones, and I am going to look at each one in MUCH more depth as I go along.

Again, feel free to ask any questions, or to leave me any comments or feedback - either here on the blog or by emailing me at Taniquelle@gmail.com. I want to make sure this is as accurate and clear as possible, and I want to leave it open so that people can feel free to discuss issues on here as much as they want.

The next post will be up soon, and it's going to deal with an overview of American Indians today - where they stand and what the scene looks like.