Ah! A football tactics and musing thread!
Where you place a player on the pitch has much to do with your team's style of play. Generally, if you aim at a fast, one touch passing style of play, it becomes more important to pay attention to your players' stronger feet. For example, if you like to play the ball long down the pitch, it's much less important to have a left footed central defender on the left and a right footed one on the right, than when you're building up attacks with short passes and the defensive line pushing up in support.
It's also important to bear in mind the particular style of play of a winger when placing them on the right or left. For example, Arjen Robben of Holland and Bayern Munich is almost exclusively left footed, but prefers to play on the right as he likes to cut inside rather than cross. David Beckham, on the other hand, one of the finest crossers of the ball when he still played in serious teams, only ever played on the right to thump the ball accurately over long distances towards the far post or target man. Rafael van der Vaart and Messi, on the other hand, are extremely strong with both feet, and started out as wingers, but both prefer to play in a free role behind a striker and make use of their skills with both feet to dribble, pass and shoot through gaps forming on both flanks by defenders backtracking to close down fast wingers.
In general, however, with weaker teams without such stars it makes sense to place wingers and fullbacks on the side of their strongest foot to keep the ball inside the lines, and pass and cross accurately forwards and towards the middle. When playing with two centre forwards, it's best to have them switching positions often enough that it doesn't really matter what side they're on. Also, when playing 4-4-2, at least one of the strikers should ideally be a decent header of the ball, which is much more useful than what foot he shoots with.
For women's football, substitute the above 'he's for 'she's.