How to anticipate the opponent's next move

I know that when you are planning your next move, you should take the opponent his position into concideration and try to figure out his options so you can decide on your next move. 

This all looks fine but there's a couple of things I find difficult with that tought process. 

At expert level you have a very good understanding of positions and plans and what not. On my level (beginner) we make many mistakes, don't always see the best tactical option or don't always have the best plan. 

In that case, can you provide some tips on how to anticipate the opponent his next move. 
Currently I try to look what I would do if I was the opponent but concidering my level, I make blunders and many mistakes. This also reflects while trying to figure out the opponent his best move.

Sometimes by overlooking a piece I make a wrong assumption which results in a mistake from my end.