The 2 by 2 Rubik's cube does not have any edge pieces or center pieces like the 3 by 3 and the 4 by 4. All the pieces are corner pieces.
On Amazon, a two by two cube costs $6.82 for a speed cube and $4.97 for a non speed cube. If you are getting one, you should definitely get a speed cube because the pieces move so much better. This cube is a good cube for beginners and almost all the algorithms are used in other cubes. So if you want to memorize it, it would be easier than some other cubes.
The 2 by 2 only has corner pieces. It is a beginner cube and only requires you to know R, U, R', B, F, and F's. That is, when you use the beginner method. It is the first cube that I learned how to solve. If you want to watch a video and learn using the beginner method you can use the links below.
Beginner method: https://www.youtube.com/watch?v=TaelEuJ18bA
Or use https://www.youtube.com/watch?v=zg1sK6sI--I
For a different beginner method: https://www.youtube.com/watch?v=sU_PyseFjPY