How do I know when it's time to pump up my tires?
The correct tire pressure for you is typically not whats written on the tire sidewall. That's an arbitrary number determined by the marketing and legal departments at the tire manufacturer, not the engineers (usually it leads to an overinflated tire, which can damage the wheel and reduce control of the bike). You'll have to play with the pressure to get a properly inflated tire. Various manufacturers have rough guidelines for what pressures are good based on weight and tire size, but they're just guidelines -- you have to play with it on your own, since tire pressure is a personal preference (given that it is not under or over inflated --  a properly inflated tire absorbs hazards, doesn't pinch flat and has low rolling resistance, whereas an under inflated tire can pinch flat and also damage the wheel). A rule of thumb is that the rear tire should be 10% higher pressure than the front due to the load difference. You may also use different pressures depending on season or other conditions. 

As for how often you need to check your tire pressure, note that unless the tire is severely underinflated, you won't notice it by visual inspection or by just pushing on the tire (depending on what pressures you're running). I'd suggest using a floor pump with a pressure gauge and associating proper inflation with particular pressures for a given tire.

You lose pressure from road hazards (e.g. if you hit a bump, some air might come out) as well as leaks (inner tubes and tires are porous to some extent, and valves leak a bit). The rate at which you lose air depends on your components and your rides. Ideally, you'd check before every ride, but for most people, weekly is a good enough option.