Solving 2x2 Rubik's cube

Base combinations

1. Swap FRU <-> FRD - R U R' U' (with rotation)

   Repeat, and cubes are back to previous places but rotated. Repeat 6 times changes nothing, everything comes back to original places

2. Swap FRU <-> FLU - U R U' L' U R' U' L U (with some rotation)

   The D layer stays unchanged, the BRU and BLU rotate too.

Base algorithm

1. Build one layer, it becomes D-layer for now, should be easy enough w/o any explicit algorithm.
2. Use combo 2 to place the cubes of U layer in the correct places, disregarding their rotation for now.
3. Turn the cube upside down, the already built D-layer becomes U-layer.
4. Start rotating the now D-layer using combo 1 x2 or x4 - do not worry that U-layer becomes undone.
5. w/o rotating the whole cube, use D or D' to place the next incorrectly rotated cube of D layer to position FRD.
6. Repeat step 4 and 5.
7. Apart from some U or D rotation it should come together eventually when rotating the last incorrect D-layer cube.

Source.