Solve the last triple of the first two layers. The beginner version solves piece by piece. In the intermediate version the triple is solved in two steps, and an advanced version solves all three pieces using a single algorithm.
The first part of solving the last triple is to place the corner. This is a simple insert using either F' U F or BR U' BR'. Check the orientation of the corner then insert using the appropriate algorithm. If the corner is in its correct location but misoriented, use either of the two algorithms to bring it to the upper layer, then correctly solve the corner.
F' U F
BR U' BR'
Next, the bottom triangle will be solved. This involves using three simple algorithms that move the corner that was just solved out of the way, places the triangle, then restores the corner. Do a slight horizontal rotation to have the right side layer in front and the algorithms can be executed similar to F U R U' R' F', F R U R' U' F', and F r U R' U' R r' F'.
R U BR U' BR' R'
U' R BR U BR' U' R'
R br U BR' U' BR br' R'
The last step to solving the triple is to place a right side triangle above the corner. There are three to choose from so they will be easy to spot. Use the correct algorithm depending on if the triangle is to the left or right of an edge on the upper layer.
U' BR R BR' U BR U' R' BR'
U F' R' r U' r' F R F
Once accustomed to the starter steps, the first two parts of solving the triple can be combined. The corner and bottom triangle can be simultaneously solved using one of 23 algorithms. Go to the document below for the complete algorithm list.
The most advanced version of solving the triple is to solve the three pieces all at once. The full set can be learned from the following algorithm document.
To reduce the number of cases for the last triple, it can be ensured that the corner isn't placed in its slot before arriving at the step. At the end of solving the centers, solve the centers in a slightly different way to keep the last triple corner on the upper layer. If the corner is attached to the end of the half center and would be placed in slot with the R U' R' or R U R' ending, the corner can be moved out of the way. Below are the two main alternate endings to prevent the corner from being placed in its slot.
R F' U' F R'
R BR U BR' R'