I've been to the Eagle's Nest three times, all on my own. I, personally, would never do a tour. Doing it yourself is too easy to spend money on a tour. I've also spent a lot of time researching it on the Internet.
There is a bus, RVO 840, the Watzmann Express, that leaves hourly from near the Salzburg Hbf and makes a number of stops (like at Mirabell palace) on it's way out of town. It goes to the Berchtesgaden Hbf. From there you can take another RVO bus to Obersalzberg where you buy a ticket for the special mountain bus that takes you up the private road to the Nest (actually, admission to the Nest is free if you want to hike all the way up to it). The ticket for the bus also includes use of the elevator from the bus parking lot to the actual Nest.
However, if you are not as adventuresome or as skilled in getting around in Germany as I am, or if you just don't want to take the time researching it yourself, you can do it with a tour. I've heard good things about the Eagle's Nest Historical Tour, so I would recommend it. It's based in Berchtesgaden and run by David Harper, an American, and his German wife, so they speak English. The tour leaves from there offices in Obersalzberg, so you'll also need to take the bus from the Hbf to Obersalzberg.