Buying bitcoins is much like buying stocks. You establish an account with a trading company called an exchange, you put money into your account on the exchange, and you trade someone else that money for their bitcoin. There are exchanges that make that quite simple, even ones that do it by using your credit card to buy bitcoin like it’s a regular purchase. You can also just buy bitcoins from a friend in person, and in some places you can get them from a bitcoin ATM.
You “cash them in” in the same way you bought them. You go to an exchange and trade someone your bitcoin for their dollars, and then withdraw the dollars to your bank account. You can also sell bitcoins to a friend in person, or use your bitcoins to buy stuff from a store like Furniture, Bedding, Jewelry & More (Overstock) or Purse (Amazon). And you can get money from a bitcoin ATM.
What makes the market fluctuate is the same thing that makes all markets fluctuate: a difference between supply and demand. If a store has lots of hammers and nobody seems to be buying hammers, the store lowers the price for hammers. If a hurricane is coming and lots of people want hammers, the store raises the price for hammers. Same for stocks, same for bitcoin.