Section 1: How to get the tripod.
This step is pretty intuitive. Two get the base and the first two legs you can use CFOP, Petrus, ZZ or LBL. For the last leg you could make a corner-edge pair and then put another edge in.
Section 2: How to finish.
Method 1: F2L slot then TLL
F2L Slot
Mostly intuitive, might add stuff later.
TLL (Tripod Last Layer)
Consists of solving the last 5 pieces in the Last Layer.
Here are Some one look Tripod LL algs. I am still in the process of making this so if you know any good algs let me know.
You can also solve this in two looks by solving edges then corners using commutators.
Method 2: edges first then corners.
Edges
Can be done intuitively minus parity (the swapping of two edges) with different variations of the sexy move.
Parity can be done with a J or V perm or with one of the following algs.
U2 R' U R U2 R' L' U R U' L
L' U R' U' R L U2 R' U' R U2
R U2 R' U' R U2 L' U R' U' L
L' U R U' L U2 R' U R U2 R'
Corners
The corners can be done in one kind of like COLL and also in two looks with solving the bottom corner then solving the finall three with commutators.
Section 3: Tips and Techniques.
1. on the final leg of the tripod it's some times easier to have it not be matching.
2. while finnishing the last F2L you can cut down on half the cases by orienting edges.
Section 4: Probability/case number area.
There are 105 cases to solve TLL and there is a 1/108 chance of getting skip.
If you have TLL with edges oriented then there are 51 cases with a 1/54 chance of a skip.
The chances of getting a skip on the third leg of the tripod is 1/150 and with edges pre oriented it's 1/75.
There are 72 cases for the last F2L slot and the probability of skipping is 1/72.
With edges oriented for the last F2L slot there's 36 case with a 1/36 chance of skipping.
Section 5: External links.
Speedsolving: Tripod Tutorial
Speedsolving: Tripod Method
Speedsolving: Optimal Tripod Finish Analysis
Speedsolving: Tripod Finish
Wiki: Tripod Method
YouTube: Tripod Method (Rubik's Cube)
YouTube: Tripod Method for the Rubik's Cube (#2)