Just last week, Monday morning, my husband found out that he had a property tax lien on his Transunion credit report that did not belong to us. I called Transunion's credit disputes phone number (found under the contact link on their website), went through a short phone tree, and spoke to someone immediately. I told the rep what was going on, and he made a few notes on why I claimed this was not our lien and said the dispute was now open.
Their process starts by contacting whatever company or organization originally reported the information to seek confirmation of it's validity. That company then has 30 days to respond. If they do not respond, the disputed item is deleted. Once Transunion was the necessary information a decision is made and the dispute is closed. They then mail a letter disclosing the results of their investigation. Our dispute was decided in our favor two days after I called. They took two days to mail the letter, which reached us two days after that. All told, we knew a week after I called.
I chose to call, as I wanted to talk directly to a person in order to make my case clear and ask any questions. After I'd opened the dispute, I tried seeing what opening a dispute online was like, but the system said it wouldn't work with the data provided and I'd have to call, so I don't know if online will work for you. I called Transunion twice, and both times immediately got someone on the phone, so I'd try that before mailing in a dispute if I were you.
Of course, as another poster said, the time a dispute takes is going to depend on what needs to be disputed, and how quickly the company that has to verify the information responds to the credit bureau. I've read that you can mail in your own supporting documents, but I chose to let the credit bureau do the leg work to start. In theory, though, it shouldn't take much more than a month. Even if an item isn't detrimental to your credit, I think it's worth trying to remove it. Good luck!