Most players have a naturally stronger foot they prefer to dribble and shoot with. Few players are equally as strong with both feet.
This impacts the optimal position for the player to play in and how the team chooses to execute set plays, in particular free kicks and corner kicks.

Positional Play:

Keep it simple. Play the player on the side of his/her strength. Left footers play left defense, left midfield and left forward. Right footers on the opposite side. Some coaches like players playing on their off-side, but that only makes it difficult for the players.

Set Plays:

Here is where there are real options.
Right footed players crossing balls in from the right will typically hit "outswingers", i.e. the ball curves away from the net, sort of in the shape of a banana.
Right footed players crossing balls in from the left will typically hit "inswingers", i.e. the ball curves towards the net.
The same is true for left footers from the left (outswingers) and right (inswingers) sides.

Corner Kicks:

If on a corner kick from the right, you want the ball to curl away from the goalkeeper, have a right footed player take it. If you want the ball to curl towards the goalkeeper, have a left footer take it from the right side.
The decision is based on where you want to apply the pressure and which runs the other players are making to get to the ball.

Free Kicks:

On free kicks near the penalty box, where a wall is in place, similar thinking applies.
If the free kick is from the right side (when looking at the goal) and you want to play a cross curling away from goal towards the far post, use a right footed player. If you want the ball to curl toward the goalkeeper, use a left footer.
If you want to take a shot on goal, bending the ball around the far end of the wall, use a left footer. If you want to take a shot around the near end of the wall, use a right footer.
Again, the opposite is true from the other side.