Is there a good method to solve this kind of Rubik's cubes?

Question

In the office's kitchen we have a 3x3x3 Rubik's cube that is, well, unusual: instead of simple colours on the faces, there are pictures.
While solving the rest of the cube is no different from standard ones, the orientation of the central piece of each face is crucial, as it is immediately apparent when they are not oriented properly, since the figure will appear "broken".

So the question is: are there good methods (or algorithms) that a neophyte can pick up and use to solve this cube properly?

disclaimer on my abilities: long ago I was able to solve regular 3x3x3 cubes going by layers, and having no internet, I basically had to come up with the move sequences by myself each time. It was taking days sometimes, but it was fun. Yet, this means that now I have issues following the instructions I come across the internet, since a sequence of letters does not explain me exactly what I am trying to achieve, and I cannot visualize the expected intermediate result before executing the sequence.
Hence, I would greatly appreciate answers that will explain the concepts, rather than giving me a list of algorithms to memorize, but if that is not possible, I will accept what is available.

Answer 1

In your standard layer by layer method, you presumably start with a cross, i.e. the four edge pieces in one face. It is fairly easy to make sure that whenever you solve one of those four edges, the two adjacent edges are correctly oriented. In this way you will have 5 of the 6 centres correct. When solving the rest of the first two layers, those centres will stay intact.

Solving the last layer can be a bit trickier. Some of the algorithms that layer-by-layer systems use will disturb the already solved centres. However, if you method does not disturb them, then you should be able to solve the pieces by placing them correctly relative to the final centre. If you have a cube where one of the centres does not have visible orientation, then it is useful to let that be the final face so that you don't have to worry about it.

Alternatively, you can solve the cube normally and fix the centres at the end. There is one easy to understand way to twist two centres, provided you know the 6-spot pattern and the 4-spot pattern:

1. Find a twisted centre and determine how it needs to be rotated.
2. Rotate the face with that centre that amount (so the centre is correct but the pieces around it are wrong).
3. Do a 6-spot or 4-spot pattern to replace that centre by another one that needs to be twisted.
4. Rotate the face back the way it was.
5. Undo the 6-spot or 4-spot pattern by exactly reversing the moves you used.

This allows you to twist any centre by any amount, as long as you twist a different centre the same amount in the other direction.

(You can shave off a few moves by not doing a full 6-spot or 4-spot, but only doing just enough to replace the centre of one face by another.)

Twisting a single face centre is trickier, and I'm afraid I will have to use letters for the moves. A single centre can only be twisted by a half turn. Basically you have to give that face a half turn and then swap opposite edge pieces and opposite corner pieces in that layer.

Consider this move sequence: R L U2 R' L' U2
Let's call this sequence X. In the top layer (the U layer) X swaps one pair of opposite corners, and one pair of opposite edges. The other two corners and two edges stay in place. The rest of the cube is mixed a bit.

Now consider what happens when you do X U X' U'.
The first X swaps two edges and corners, the U replaces them by the unswapped corners/edges, the X' then swaps those as well (while also restoring the rest of the cube), and then U' puts the top layer back again. So this puts all the pieces of the top layer in the opposite place, without twisting the centre. By following this with a U2, everything is back in place and only the centre has twisted.

There are a few move cancellations:

X U X' U' U2 = (R L U2 R' L' U2) U (R L U2 R' L' U2)' U
             = (R L U2 R' L' U2) U (U2 L R U2 L' R') U
             = R L U2 R' L' U R L U2 R' L' U
             = (R L U2 R' L' U)2

Answer 2

Use a method of your choice for solving it as though it is a standard 3x3. Once it's only the centres that are messed up, just continue to repeat a single algorithm that only rotates adjacent centres.

The following algorithm rotates the centres of the U (top) and L (left) faces.

$V'H'VUV'HVU'$

The same site also lists a way to rotate a single centre upside down.

$URLUUR'L'URLUUR'L'$

Where:

$V$: move the centre vertical slice upwards.
$V'$: move the centre vertical slice downwards.
$H$: move the centre horizontal slice to the left.
$H'$: move the centre horizontal slice to the right.
$U$: rotate the top side clockwise.
$U'$: rotate the top side counter clockwise. $L$: rotate the left side clockwise.
$L'$: rotate the left side counter clockwise. $R$: rotate the right side clockwise.
$R'$: rotate the right side counter clockwise.