I usually apply the following rules as guidelines. I'm far from being an expert, so follow them at your own risk. There are a lot of better guides on the internet for reversi. Search "reversi strategy".

Most strategy sites have some version of my chosen rules, not necessarily in the same order.

1. As far as I'm concerned, the most important point is to avoid having clump edge stones. I explain the concept: in reversi opening we have a central clump of stones, yours and the other guy's. The idea is to have as few stones as possible on the outer edge of the clump. Of course, each move forces you to put at least one stone on the edge, but try not to flip stones along the edge.
2. You must try to have your stones connected as one area. As a consequence, the opposite rule: a move that splits your opponent's area is good.
3. Try to have AS FEW STONES AS POSSIBLE, until quite late in the game. (Of course, do not go to the extreme of zero stones ). Most sites state this as rule number 1. I apply it too, but give it a lower priority.
4. Avoid putting stones on the edge of the board, as late as possible.
5. As a general rule the corner positions: a1, a8, h1, h8 are good for you to capture, but beware: not at any price.
6. As a consequence the squares next to the corners are to be avoided until late in the game: a2, b1 and so on. particularly bad are b2, b7, g2, g7. There are exceptions, however.