Well, if you follow these steps, you'll be there in no time! Let's get started
DISCLAIMER: My 2x2 happens to have black instead of white, don't let that get you confused :D
Step 1: Starting Out
Step 2: Getting the Black(white) Side
Step 3: The Yellow Side
--end of picture 1
Now line it up with its correct sides as it shows in picture 2
--end of picture 2
Then, you will use this algorithm: R, U, RI, U, R, U2, RI. Then organize the cube like you did above and keep using this algorithm until the top is all yellow.
--end of picture 3 and 4
Step 4: Fixing the Corners
After they are matching, put the two matching sides to the back of the cube and do the same algorithm until you complete the cube :)
Step 5: Celebrate
Anyways, congrats. You solved the 2x2. Are you ready for the 3x3? Check my instructable on it!