Step 1: White Cross
You should be able to complete this step just by playing around with the cube. Make sure that the edges of the cross match the center squares on the adjacent sides.
Step 2: Finish First Layer
Step 3: Middle Layer
You may need to move some middle layer edge pieces from the top layer. Follow the patterns below to get these pieces in the right places.
Step 4: Top Corners
To get the corners in the right place you can use this pattern to swap corners until all 4 corners are in the right location. At this stage they do not need to be facing the right way.
To orient corners use a combination of the patterns below. The first will turn the faces of three corners clockwise. The next will turn the faces of three faces counter-clockwise.
Step 5: Top Layer Edges In The Right Place
Make sure all the edges are in the right location. Do not worry if they are facing the wrong way. Use a combination of the patterns below to move these edge pieces.