When I buy a plane ticket,after I get on the plane to where I'm going, do I buy another plane ticket to get back home later or can the ticket I bought to get to my destination also get me home? I've never been to an airport or had to purchase a plane ticket before.
It's common to purchase plane tickets as a round trip: a single purchase that includes a ticket to your destination and a ticket back home. When you search for plane tickets online, the default option is usually a round trip, and you'll enter the date you want to depart and the date you want to return and then choose both flights as part of your transaction.
It is also possible to buy one way tickets. Two one way tickets may sometimes cost more than the same flights as a round trip, so this is generally less common.
Plane tickets often get more expensive close to the travel dates, and they can sell out, so many people buy a round trip ticket in advance, rather than waiting until they're at their destination to buy a ticket home.
In some cases if you're crossing international borders, you're required to have "proof of onward travel": another ticket that will take you back out of the country you're visiting, so they know you have some intention of leaving.