Wes & Preeti
TOP CORNERS
Now that you have the top edges in place it is time to line up the corners. Your goal when finished with this step is to have the cube looking like this:

You can either decide which of the 4 corner pieces to put in place, or simply locate one and move it to the proper position. An important thing to remember is to keep the edge and center pieces aligned. Because we have set the 4 top edge pieces, any move you do that takes them out of their current position must later be reversed to put them back. You must be careful about any rotations you do other than moving the bottom layer (D). For this reason it is easiest to move the corner pieces to the bottom layer then rotate them around to get them into a staging position for placement into the top layer.

Let's take the yellow/red/blue corner piece as an example. This piece needs to be placed in the top layer at the point of intersection of the yellow, red and blue sides. Hold the cube with yellow on Top, red on the Front and blue on the Right. The piece needs to go into the upper right corner of the Front face. As long as it is placed with the yellow side on the Top face, the other 2 sides will fall into place.

Similar to the edge pieces which only have 2 orientations, the corner has 3 - one for each color. What we want is to move the the piece so that the yellow side is not on the Up or Down faces and then rotate it to the bottom layer. Remember that any rotations of and side other than the Down side must be reversed later to preserve our edge alignments. Below are examples of where the yellow/red/blue piece may be and how it can be moved into its proper place.

 D²_F_D'_F' R'_D_R_F_D²_F' L_D²_L'_F_D'_F' D²_R'_D_R

Let's walk through one of these in detail. Essentially you need to get the yellow face into 1 of 2 positions and then rotate it up into the top layer. You want to have yellow facing out in either the bottom right corner of the Front face, or in the bottom left corner of the Right face. Here is a detail of the first example given above.
 D D F D' F'

Looking at figure 1 shown above you can see that the yellow side can be moved to the bottom left corner of the right face with a movement of D. In figure 2 we have moved D. If we now performed move F' the piece would be in place, however we would have ruined our alignment of the yellow/red edge piece. For that reason we move D a second time to move our piece out of the Front side as shown in figure 3. Since what we want to do is move F' to put the yellow piece up top and we always have to undo any rotations of any side other than Down, we start by moving F in figure 4. Now we can move D' to put the yellow piece back into the bottom left corner of the Right face as shown in figure 5. Then we undo our Front rotation by moving F' in figure 6. This puts our piece in the right place and maintains our edge alignments.

You have to think a move or two ahead. Since we always have to undo any rotations that mess up our previous alignments it is easiest to first make a move in the opposite direction from what our final move will be, position our piece and then undo the 'bad' rotation.

Here is the example using the java applet.

 D²_D_F_D'_F'

Continue using this methodology to place the remaining 3 corner pieces into the top layer. Once finished you are ready to move on to Solving the Second Layer.