You can find your fines in LUBcat. Log in and go to "your fines". The date shown is the date you returned the book. You will see the title of the book, the library which it belongs to, and how high the fee is.
If you have more than 100 SEK in fees you cannot borrow another book until you have paid. The fine has to be paid at the library owning the book (you can see it next to the title). You need to return the book before you pay the fine.
Note that the method of payment can vary between libraries: some only take card, others only take cash.