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 (where you have to click "Sign In" and select "My Library Account".
If you have any books checked out, you'll see the in a box called "Loans", and you can also see other options like "Requests", "Fees", etc. You should see a due date. You should also be able to renew an item.
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.