I sometimes feels as if the laws are there to protect the tenant, even those who abuse the lease agreement. What everybody else has said is true, each state has its own way of doing things.
But, be forewarned, I don’t believe any are a simple as go down and get a piece of paper and then get the sheriff to kick him out.
All are going to require going to court and all are going to require things be done in a specific order. All will take time, sometimes months.
Here is a good site outlining how we have to do it here in Texas. I have never had to go beyond the Notice to Vacate myself, perhaps because we do as much checking on the tenant before they sign a lease as we can and weed out the bad ones. The act of handing over the Notice or, if they are not there, posting it on the inside of their front door has always been intimidating enough to get them moving. Never go alone, always have at least one witness with you. it is even better if he is about 6’-6”, 250 lbs and named Vito or Bubba Because we are required to give them 3 days to get it together we usually do it on a Wednesday and give them until Monday to be gone. Our theory being, if they have a couple of days to find a temporary place to stay and the weekend to move it is more likely they will just leave.
If you are dealing with someone who is not on his/her first eviction, they will know what you can and can’t do and are probably used to gaming the system in which case you are in for a long drawn out process If not, sometimes the threat of eviction and/or legal action, including getting the police involved will be enough to get them moving out. Since you have already done the pay or quit thing to no avail then you may have to go the court route but it doesn’t hurt to try to intimidate them further. Here in Texas we can file the paperwork for eviction the day after the rent is late. We don’t, but we could and at some point it will save us time.
Your unit will probably be dirty and damaged, One suggestion I have for you is that if your lease allows you to go into their unit without them present, do so and take dated photos or videocam the entire place. That way any malicious damage that occurs at the end can be documented and then, for all our sake, take them to court and sue them for the damage.
And, if they leave without paying you back rent, at least they are gone and you can get it back on the market..