Call the bank and ask to split the account. In most cases, a bank will require you to close the joint bank account. It will then permit you and your previous joint account holder to open up new personal accounts--provided that you qualify. Bank policies differ, however, depending on the bank.
Wait for all current transactions pending to the joint bank account to clear. You can close a bank account regardless of whether transactions are pending, but doing so may leave you to pay fees for debits or checks that posted after your account was emptied and closed.
Withdraw the money in the joint bank account and allocate it between yourself and your joint account holder.
Apply for a new bank account in your name only. Depending on the bank, you may need to undergo a credit check to open up a new account.