Inflation can indeed be caused by supply and demand, which is what you're referring to. However, if an open market is allowed (no price controls), generally supply will rise to meet demand and price will fall back.

Unfortunately, inflation can also occur when too much money floods a system. We see this in the case of college tuition. Giving college loans to anybody with a heartbeat floods the system with money, causing tuition price inflation.

This does happen with countries as well. Every dollar that a government borrows and then spends, is money creation. The act of selling the treasury notes allows them to obtain money today for the promise of paying it back with interest in the future. That new money is spent into the system and much of it takes the form of bank deposits which can then be inflated 10:1.