When I learned to solve Rubik's Cube around 1980, I consulted two different books (among many available) that described algorithms -- comprising a string of "subroutines" (to borrow a computer programming term) -- that always led to a solution. They were similar in approach but different in detail. I ended up choosing one book's method but writing it down & learning it using the other book's notation system, which I found easier. In all the methods I've seen, you don't do one SIDE at a time but rather one of the three LAYERS at a time. The top layer has 4 side pieces and 4 corner pieces. The middle layer has 4 side pieces. The bottom layer is like the top. Which color you call top is arbitrary, but once you choose it you stick with it. It gets harder as you go, because any moves that progress toward a solution have to preserve what has already been accomplished. If you go top-to-bottom, the bottom layer is way harder than the top. It helps to understand the basics of the cube first. If you take one apart you see that centers of the six sides, each a different color, are already placed in a fixed relation to each other. That's why you never work on a center color -- always one of the side pieces (having two colors) or corner pieces (having three colors). Also, when placing a piece you have to mind both its position and its orientation. So if you're trying to place the green-yellow-red corner into one of the cube's 8 corners, where it belongs, there are also 3 possible orientations, only 1 of which is correct. Often you manipulate a group of pieces with a single subroutine. If you're serious then get a book & prepare to waste a lot of time!

The usual way is do all of the *white* face first - and that means getting all the colors on the mini-cubes in the white face in the right place, not just the white side alone. Then turn the cube over and keeping that face correct, do the remaining corners and the edges adjacent (in either order). Then do the edge pieces on the bottom face. I invented a move which can do all the edge pieces on the cube: This is it: Center, Center, Bottom, Center, Center, Bottom, Bottom, Center, Center, Bottom, Center, Center. Center means rotate the slice between the left and right halves of the cube 90 degrees. Bottom means rotate the Bottom face of the cube 90 degrees. (pick a direction and stick to it). This swaps three particular edge pieces and flips two of them. By first moving the three pieces you want to swap into that shape, then doing the move, and then putting them back, you can swap any three you like. You can swap without flipping by doing an extra "Center" move before you start. You can swap two by swapping three including the two, making sure you don't put either of the two in the right place, and then looking how to sort out the three you have left. Unfortunately I can never remember how to do the corners.