How do I determine what types of maintainence I need to perform?
Know what pressure your tires should be at (range is written on the sidewalls). Check and re-inflate tires to proper pressure every ride, or every couple of days if you are riding regularly. You'll soon find out how often tires need some air.

Check and adjust brakes.

Clean chain, sprockets, idlers, chainrings; re-lubricate the chain. How often depends on how much you are riding and in what conditions. 

Generally keep the bike clean.

Adjust derailleur indexing as needed. Check chain wear.

Periodically, check for rattles, and anything loose. Once a bike starts to get some miles on it you can check headset, bottom bracket, wheel bearings for play. Make sure pedals are tight in the cranks. Check wheel rims are true.

Eventually you start wearing things out: brake pads, tires and chain are the primary wear items. If shifting accuracy is suffering changing out cables and housings is necessary. Brake cables and housings can also be replaced. 

There are plenty of guidance videos on YouTube to help you with specifics of all of the above. Personally I like the Global Cycling Network Tech and Park Tool's YouTube channels (and articles on their web site). I'd definitely recommend learning how to clean you bike properly as it has a substantial effect on how it performs.