Cashing a check without having your own checking account can be hard but it's not impossible either.
Try looking for check cashing places that cash checks for a small fee, Walmart will sometimes cash checks for a small fee.
Or if you have a friend that has a checking account you can sign the check along with the person and cash the check using their checking account if they have enough funds available in their checking account to cover the check.
You can also go to the bank that issued the check and see if the bank that the check is drawn on will cash the check for you.
Some banks will cash checks for people without a checking account if the check is drawn from that bank because that bank should be able to verify if the person who wrote the check has the funds to cover the written check.
You can also endorse the check over to a friend and they can give you cash and then the friend can deposit or cash the check using their checking account.