How Do I Get My Room Mate Evicted

I recently rented out my spare bedroom to a young couple that had relocated to Florida from PA.
They paid $650 up front for a 30 rental. No agreement was signed Nor did they ask for a receipt for the money they paid.

Everything seemed ok at 1st. Since they started staying here, thay play music at all hours of the night
I haven't been able to sleep. They leave water running & leave lights on. I have asked them on several occasions
to turn stuff off & keep the music down, But the reply is always the same,
"I can do what ever I want because I pay rent just like you"

I have informed them that our living together under the same roof is not working & they need to find another place in which to live. He keeps saying I don't have to move, as I pay rent like you do.

I am the sole person on the lease for my house.

What legal recourse do I have & how do I go about evicting this couple?

they are your tenants. You must terminate their tenancy as the laws of your state requires (most likely a 30 day notice). If they fail to leave at the end of that time, you would have to sue to have them evicted.