Call up the website of the theater. If you don't know the name of the theater, do a general search with the name of the film and the city. That search should turn up the names of any theaters in the city showing that film. Click on the link to the theater.
Click on the name of the film you want to see. Most chain websites will also show the screening times that day. Click on a starting time, or, if you want the ticket for another day, click the box showing the date. Keep clicking until you get to the day you want.
A click on a showtime will bring up the ticket purchase page. For some theaters, this page will belong to a ticket company like Fandango. Fill in the number of tickets you need, confirm the order, and check out. Some sites accept Paypal, but all will accept a credit or debit card number.