What is a quite title petition

A quiet title petition relates to real estate and is used when there is a cloud (not clear ownership) on the title that won't allow it to be sold.

I answered this question earlier. Here it is again:

A quiet title is a legal proceeding. It happens when there is a piece of property where the ownership is in question. A person (usually the one who has the best claim) files a lawsuit to quiet title. Anyone who may have a claim to the property is notified and given a chance to show the court why their claim is better than anyone else's claim. After everyone shows their proofs the judge decides who has the best claim and ownership is awarded to them. That makes the quality of their ownership "good and marketable" and then they can get a title insurance policy and finance the property or sell it.

Can I do the quite title action myself. Or do I have to pay an attorney to do it for me?

If you did not have to ask, most likely you could, but since you will have to be doing title searches to even know who to notify that may have a claim, and then show and prove they don't have one.
So you basically risk the judge giving a legal lien onto the property or even claiming your purchase not valid. So you want an attorney to do this if you don't know exactly what you are doing