1) Order a copy of your credit report (from Experian, Equifax, and Transunion– they are required to give you a free copy once a year)
2) Determine which reports are showing the eviction record
3) Send a certified letter with copy of report to all 3 credit reporting agencies (individually) The letter will need to dispute the eviction and provide some type of evidence as to why the record should not be on there. (a copy of your court case showing that you won and were not at fault should suffice. You can also contact the attorney that handled your case and have him write a statement that will show why the eviction should not be on the report.)
4) Then, within 60 days the credit reporting agencies are required to review the dispute and remove the record.

That’s all you need to do. The sooner you start the quicker the record will be removed. If you need additional proof, you could also consider filing a complaint with the Rental Protection Agency. You would do that to show that the eviction was reported falsely, this would allow the RPA to have an unbiased 3rd party confirm your story, thus making your case for removal from your credit report solid.