This can be done with the chain on the bike. If the chain is filled with sludge, however, you'll need to remove it and use a solvent. Recommended tire pressure is usually printed on the sidewall. In general, high pressure clinchers and training tubulars require about 110 psi. If you're in doubt, call a bike shop.
Most floor pumps with a built in gauge are reasonably accurate.
The pumps at gas stations are risky to use because they quickly deliver a large volume of air, which can blow out a bike tire. Once you've established your weekly maintenance routine, the work will take only about 20 minutes. This small amount of time pays off big in confidence, safety, and smooth, efficient riding.