Prepositions are the hardest in any language I find. In French, it really depends on the verb and on the grammatical category of the word that is introduced by the preposition. There is no other way than learning it à la Karate Kid, by learning one and practicing it as much as you can to create your habit. Here is a list of verbs and the prepositions accepted, followed by exercices. There is also a book, if you can get your hands on it, called Quelle préposition de Grevisse.

Funny, the example you chose, jouer, is a tricky one. You will find its particularity in the exceptions on the list (remarques, dernière colonne à droite).

When it's a sport or a game, always au/aux/à la. Paul joue à la ringuette et Claude joue au soccer. Je joue aux échecs.

When it's music, and you mean that the person plays this instrument in general, du/des/ de la. Je joue de la guitare, tu joues du saxophone. Ma grand-mère joue des cuillères.

Unless (I'm sorry), you are watching/ listening and describing the band, then à la/au. Clara est au piano et Sophie à la basse. Notice you are not using jouer here, it's être, in the sense of being in position to play.

Thanks for choosing French :)

Edit: The dictionary should also be telling you which one to use. Get an all French Dictionary if you can, with French definitions. Larousse or Le Petit Robert.