Self-Service Removal. There are a few blacklists with a self-service removal feature that lets you take your IP address off the list without much trouble. However, you'll want to make sure you've resolved any issues before doing this. If you don't and your IP address gets listed again, it won't be easy to get it removed that next time.
Time-Based Removal. Most blacklists have a built-in, automatic process that removes lower-level listings (IP addresses that are light offenders) within a week or two. But if the IP address had sent spam more than once or did a high volume, the time period will be longer.