Open the hood, run the engine, and observe the various belt(s) and pulleys. A ribbed belt should have not motion/flexing fore-aft. If it does, stop the engine and see if it's properly installed on each pulley. If it's only one groove off, it will still work, but transfer power poorly and wear out unevenly & prematurely.
Most late-model cars have a single ribbed belt with a spring-loaded adjuster, and although you can't change the belt tension, you can check it with the built-in tension indicator on the spring housing. If there's no indicator and the Owners Manual provides a specification for belt tension, use a professional-quality gauge made for ribbed belts to check. For a conventional V-belt, you'll need a different gauge.
In either case, the adjustment can be done with a jackscrew. Loosen a locknut and then turn the jackscrew to increase or reduce tension. Some car manufacturers provide a specification for belt deflection instead of belt tension, but it's more difficult for a non-mechanic to measure this accurately.
If any pulleys wobble, they are loose or mis-aligned. This affects their effectiveness but may also cause a belt to pop off, and even damage the attached accessory. Misalignment is often the cumulative result of several deviations from manufacturing tolerances, and can be fixed by shimming a pulley or the accessory's mounting bolts.