I've been told my IP is being used to harass someone. They know its not me but can't be bothered to explain how it happened or how I make sure it doesn't happen again. I'd appreciate any help. Thanks much.

The IP address in question is NOT your property, but that of your ISP.
So if there is an issue with the someone using that address then the ISP are the ones that should be involved. They have well define policies on how to deal with abuse.

Who is telling you this and how do they know the IP is yours? This sounds like a scam.

If you connect to the Internet using a broadband connection, then your IP rarely changes. But you can force a change sometimes but disconnecting from your ISP for a few days. Or you can request that your ISP reset it.

Your IP is assigned to you when you connect to the ISP. This is usually done dynamically. But your ISP will generally try to issue you the same one if you log back in within a few days.

If you have a dynamic IP yes it could be used by anyone. However, then you wouldn't have to worry about it at all. If someone claims that another person is using your static IP, then this should be coming from your ISP. Otherwise, they couldn't have this type of information. If it's not your ISP who is telling you that, you should ignore it. If you still want to make sure you are safe, then call your ISP and tell them about it. They are able to see the MAC addresses related to the connection from your IP.

I called my ISP (AT&T) this morning and told them about this thanks to all your replies. :) They pretty much told me what y'all said, it's not a static IP address, routinely changes and if anyone had problems with a certain IP address they should contact them not me. They also told me no one has contacted them about this matter and I know it's not ME so I'm just going to ignore it.

Thank you SO much for your help. I was really freaking out about this, LOL. :)

You still didn't answer WHO told you this.

I'm sorry, I missed the WHO part. It was a private investigator from a legit agency. Hence my concern.

Thanks again for your help. :)

Well he clearly doesn't have a clue what he is doing.
As already mentioned this is nothing for you to worry about, unless of course you have been doing the harassment..

ISP's do NOT routinely give out IP address information without court order.
All in all this sounds like a scam.

Hmmm. As CurlyBen said, this guy doesn't seem to have a clue. So, if I understand you, this PI contacted you, out of the blue, with some story that your IP was being used to harass someone. How was this contact done? Did you receive a phone call, letter, what? What was the purpose of the call, to get you to stop. Threaten legal action, what? Was there any indication who was being harassed, and how were they being harassed? What were you supposed to do with this info? How did you determine the agency was legit?

I still don't think you need to be concerned, because this does not seem legit for the reasons we've explained. But the fact is that you have been targeted by someone for some reason. And I think you may need to get more info to deal with it. If you answer my questions we can advise further.