Gather up all the books you wish to checked out from the library. Make sure you have your library card with you before going to the checkout area. If you don't have a library card, there are forms available for you to fill out in order to obtain a card.
When you are at the desk, tell the person that you would like to check out a book(s). The person will ask you for your card and they will briefly scan the barcode to see your contact information. They'll be looking at the number of books you'd checked out in the past and if any of those books are past due.
Just wait patiently while the library staff member check out your books. They will inform you of the date the books is to be returned. There will be a paper or stamped dated indicating when your books will be due.
You will have three to four weeks before you return your book. While the book is in your care, remember to be careful with it. The library can charge you for any damage to the book.