"au" (for masculin things) and "à la" (for feminine things) indicate what it`s made of, or what flavour it is. So here it could be translated by "with". Ex : gâteau à la vanille, pudding au riz.
"du" (for masculine things) and "de la" (for feminine things) indicate an unprecise amount of something. You can translate it by "some". Ex : Je voudrais du riz et de la sauce s.v.p. (since you can`t count rice and sauce, they are good examples).
"à" has many many uses, not just for places. It can also mean "for".
If words are used together long enough, it becomes an expression, and usually those are linked by a "à". Exemple : "machine à café" (coffee machine), des chaussures à talons aiguilles (high heels shoes) and so on.