You can see the books you've borrowed and their due dates by going to My Library Account from the library homepage or from the library catalog.
If you have any books checked out, you'll see a link that says "Items currently checked out." Click that link and you'll see when your books are due. You can also renew books there if you need to keep them longer.
Make sure you get a new due date after you click the renew button. If someone has placed a hold on the book, you won't be able to renew and you'll have to return it.