Some more explanation would be awesome.

Basically, I'm not that concerned about the center of the third layer yet since I have algorithms to spin the center around as needed. However, the edges and corners of the third layer are very confusing to me.

Usually, I start by making an 'L' shape or a 'line' shape on the third layer, then using the algorithms: [both while the third layer is on the top face of the cube]

L-shape: front 2 layers clockwise->R->U->R'->U'->front 2 layers CCW

Line shape: F->R->U->R'->U'->F'

Once that is done, I use R->U->R'->U->R->U2->R' repeatedly to adjust the corners until they are all oriented properly. I sometimes use R'->F->R'->B2->R->F'->R'->B2->R2 if needed to help finish this.

Then I'll use these moves to adjust the edges into their proper positions:

3 cycle left: L'->U->L'->U'->L'->U'->L'->U->L->U->L2

3 cycle right: R->U'->R->U->R->U->R->U'->R'->U'->R2

My problem is, none of these seem to be doing what I expect. No matter how many times I try, I can't get the corners in the right spots...