Blacklisted IP address is often caused by sending numerous unsolicited emails. Whenever a complaint is submitted to an anti-spam institution, it is reviewed strictly and often leads to severe measures like the IP blacklisting.
If your local IP is blacklisted, whenever you send an email, you will get a bounce-back message with a warning and details on what further actions you can take. Simply read the message and follow the steps provided there.
If your server IP is blacklisted, then we have most probably received a notification about the issue already and are going to clear out the issue in the fastest possible time.