Your Dad can legally endorse a check made payable to him and give that check to you. You can then sign your name on the endorsement line beneath his signature and attempt to cash it at the bank that holds the account that funds are being drawn from. Bank's call checks cashed by someone other than the named check payee "third party checks." Legally, banks do not have to cash third party checks, so you should contact the bank to find out its policy.
Your Own Bank
You can attempt to cash a third party check at your own bank. Your bank does not have to cash check's drawn against other banks, but in many cases banks allow you to if you have sufficient funds in your account to cover the amount of the check. Technically, when you cash a check against your own bank account, you take legal responsibility for that check. If the check bounces, your bank can debit your account for the money that you received when you cashed it.
If neither your bank nor the bank holding the funds will allow you to cash your Dad's check, you can only negotiate it if you and your Dad both go to the bank to cash it. Under the U.S. Patriot Act, banks must identify people who conduct transactions. If the bank requires both you and your Dad to cash the check together, then both of you must present a valid form of government issued identification and any other type of ID that the bank in question requires.
Banks require ID and place limits on the ability of people to cash checks and make withdrawals but no such restrictions are placed on people who make deposits. Therefore, if your Dad cannot go to the bank, you can deposit his check into his own bank account. You can then ask him to write you a personal check from his own account and wait to cash it once his deposit posts to his account. This prevents you from having to contend with third party check cashing restrictions.