Upvote:5
Very few airlines issue paper tickets these days. You can walk up to the counter with wad of money and get one, but that's really not wallet friendly.
You can easily book online and get a confirmation number and an e-ticket number as your receipt. Doing this at least a week or two ahead of flying will increase the chances of getting a cheap ticket. On flying day you can check in online or at the airport. At the airport you can walk up to the kiosk put in your confirmation number and the kiosk will print your boarding pass. Since it's international travel you may have to go to the bag drop off to have your travel documents verified. If you don't like the kiosk you can go to check in counter and have a real person check you in and print your boarding pass. It just takes longer. Details depend somewhat on the airline.