In the end, the inflation you and I experience is a combination of all three types.
The principle of scarcity kicks in, people are willing to pay more for something that is scarce, and price inflation is created.
Ever see an auction? People talk about bidding up the price (also called "demand-pull"). This is classic price inflation; people keep making higher and higher bids in an attempt to purchase something.
On a large scale, we see this happen when the economy is humming along; people get hired, make more money, buy more things. Companies try to capitalize on this trend by raising prices.
A common example of this type of inflation is the loss of an orange crop during the winter, and the subsequent increasing the price of orange juice (also called a supply shock).
The lack of oranges lowers the total supply, making each orange more expensive. In order to stay in business, juice producers raise their prices in order to cover the increased cost of oranges.
Another good example is when you hear about airlines raising ticket prices because the price of jet fuel increased (also called "cost push"). You may have heard of "stagflation"; it is essentially a severe form of "cost push" inflation.
Employees expect their cost of living to increase each year, so they push for raises (hence the term cost of living raise). To offset the increased wages, companies pass along the increased "cost" of their labor by increasing the price of their products and services. Which means that the costs of living increase.
So you get more money each year, but the price of stuff goes up too.
Some amount of inflation is good and means the economy is growing. However, too much or too little is bad for the economy, and controlling the amount is tricky.
If inflation is too low, then deflation can occur.
If inflation is too high, then hyperinflation can occur.
This is why you hear politicians and federal reserve employees talk about a sweet spot for inflation. Usually, the Fed tries to take actions that balance growth and inflation at a "moderate" rate.