Summarize this article:

If you assemble the pieces at random, the puzzle will usually be unsolvable. Reassemble it in a solved position instead, starting with four edge pieces of the same color. This first part is the most difficult:  Slide each edge piece into position around the matching central place. Hold them in place so they don't fall. If a piece won't go in, slide it on in a "wrong" position and twist it into place. Once the cross is made, carefully put the cube down, with the cross on the table surface. The four corner pieces on the bottom should snap on easily. They will help hold the other pieces in place, so it will be easier from here on out. Make sure all pieces are in the correct position. Push them firmly into place. You should now have one gap in the middle layer. Begin with a corner, which should attach easily, then build from it until you have two rows done. The edge pieces are easier to attach if you rotate the top layer so you can slot the edge piece in directly over the gap you left in the middle layer. Finish up with the final four pieces:  Attach the last piece in the middle layer. Attach the two remaining corner pieces in the top layer. Rotate the top layer at a 45º angle to the others. Attach the final piece. The cube can feel stiff at first after adding lubricant, but after a few minutes of working it in, you should notice faster, smoother turns. If you adjusted the screws, it can take a couple hours of use to break in the cube and check whether the tension is where you want it. If lubricating made your cube stiffer and the problem doesn't go away within a couple days, you probably used too much lubricant. Disassemble the cube and wipe off the excess.

Summary:
Make a cross of a single color. Complete the bottom layer. Attach three pieces in the middle layer. Build two rows of the top layer. Complete the cube. Scramble the cube for a while.