There are a lot of solutions to the Rubik's Cube. Many of them are complicated. Maybe this one will be to you. But for me, this is the solution that is easiest to understand and to remember. It's definitely not optimal either in terms of time to completion nor in terms of moves to completion. It consists of seven stages and six algorithms.

An algorithm might look something like: D L D' L' D' F' D F. Each letter means to turn the corresponding face one rotation. Clockwise if there is no tic mark, counterclockwise if there is. Each face has a middle piece which defines the color for that face, four edge pieces which form a cross with the middle piece, and four corner pieces which form the diagonals across that face. The faces are:

Upper layer
Solving the top layer should be straightforward. There are algorithms for it but I wouldn't recommend memorizing them; there are too many other algorithms to memorize and this stage is easy enough that you shouldn't need algorithms. All you do is pick a color and solve for that face. Start with the edges. Make sure that when you put an edge in place it matches the middle piece on the second layer. Then put the corners into place. Put them in correctly so that all three colors are on their correct faces (not just the top layer. When you're done it should look like this:

Second layer edges
Now you need to put the second layer edges into their correct positions. When you are done with this stage, your cube should look like this:

In order to do this, you'll need to find the edge you want to move on the bottom layer. You'll then want to move this piece either to the left or to the right as so:

Left   D L D' L' D' F' D F Right   D' R' D R D F D' F'

Flip cube

Now you have the first two layers solved. Just flip the cube upside down so that the unsolved layer is now the U face. This isn't even really a stage but it's here so that from now on we can talk about solving the Upper face instead of solving the Bottom face.

Upper layer edges orient

At the end of this stage you will have the Upper edges correctly oriented (i.e. with the correct color pointing up so that you can see a cross). They won't necessarily be in the right position, but that's what we do in the next stage. At the beginning of this stage, your upper face will look like one of the following:

							Figure out which of these looks like your Upper face and use this algorithm to change it to next image on the right. Repeat until you have a cross as in the final image on the right. F R U R' U' F' By the way, I use "fruit-roof" as a mnemonic for this.
[The Front face for these images is hanging off the left side.]

Upper layer edges position
Now you need to rotate the edges until they are in their proper positions (i.e. aligned with the middle pieces in the second row). What you do is spin your upper face until you have one edge correctly lined up (put that on your F face), and the other three need to rotate counterclockwise. You may need to do this either zero times if you're lucky, one time, or multiple times if the edges need more than one rotation.

R U R' U R U U R'

Upper layer corners position
Now that you have your Upper cross in place, all that's left is the Upper corners. First you rotate them until they are in their correct positions. They will probably be twisted (i.e. misoriented) but that's the next stage. Hopefully, you'll start with at least one corner in its correct location. Rotate your entire cube to make that corner be the ULB corner. Then use the following algorithm to rotate the other three corners clockwise. You might have to do this multiple times.

R' U L U' R U L' U'

Upper layer corners orient
Almost done. Now you just need to twist any corners that aren't already correctly orientied. Start by rotating your entire cube until you have a misoriented corner at LFU. Do R' D' R D multiple times until that corner is correctly oriented. Then do U (i.e. just spin your upper face) until another misoriented corner is at LFU. Repeat this until you have all corners correctly oriented. If you have multiple misoriented corners, your entire cube might looked all messed up until you finally correctly orient all of them. Don't worry about it; just keep going. Once you get all the corners correctly oriented, you might need to just spin U or D once or twice to completely solve the cube. The complete algorithm for this stage (in computer programming pseudo-code) is as follows:

while misoriented corners exist {    U until bad corner at RFU    do ( R ' D' R D ) until original RFU correctly oriented } U and/or D to completely solve