Make Immediate Deposits
Get your account in the black as soon as possible. Transfer money from savings or other linked accounts if you have that option, as that gets the money there instantly. Cash deposits likewise are credited immediately. Checks can be trickier, as banks can place holds on some or all of the amount. If you've received a personal check drawn on a different bank, you may be better off going to that institution, cashing the check and depositing the bills in your account.
Talk to the Bank
Go into a branch of your bank, or call the customer service number. Explain that you know the account has insufficient funds and that you've either fixed the matter or are in the process of doing so. If this is the first indication of the problem, or if you've been a customer for a long time, you may be able to get some of the fees waived.
If you don't catch the negative balance in time, the bank may have already closed the account. That doesn't mean your job is done. You'll still need to pay the bank to erase the negative balance. The bank likely also reported the closed account and the negative balance to a consumer reporting service like ChexSystems. If so, make sure your bank updates the report and affirms there's no longer anything owed against the account.