1.     CROSS
The first goal you have in solving the cube, is solving the cross.  This means placing four edges correctly on one face of the cube.  *Note- each edge in the cross should match it's corresponding centers.  Notice in the picture above, the White/Red edge is placed correctly between the White and Red centers.  With some practice and better understanding of the cube, this part of the solution should become easy to you.
EXAMPLE SITUATIONS
R2
*Note-  The White/Blue edge is only two face turns away.  This is an easy situation.
F'
*Note-  The White/Red edge is only one face turn away.  This is another easy situation.  The trick becomes placing edges correctly, while preserving edges you've already placed.
If there are no edges on the UP face to be preserved, this alg works:   RU'
If you must preserve edges on the UP face, this alg will work:     U'RU'
*This solution starts with the white face*
Now on to 'Step 2'...."Placing 1st Layer Corners"