Actually it is very easy to do it yourself if you want. You have to go to the local courthouse, where the property is located, and get the documents that you will need in order to do it legally. Ask a clerk there for the documents and they will give them to you, but they will NOT give you legal advice.
Once you get the forms, the form that gets the ball rolling is the Demand for Possession Non-Payment of Rent which requires payment of rent or possession of the premises within seven (7) days (excluding Saturday, Sunday, and legal holidays) after the date of delivery of notice. Yes, you can deliver that document to the tenant yourself.
If you don't feel comfortable in doing that, you can pay the court to serve it for you.After the expiration time on the service of the Seven-Day Notice you may proceed with filing the Complaint for Eviction. You will file the original Complaint with the Clerk at the courthouse. The Court must also receive a copy of the Seven-Day Notice and a copy of the lease. You must also attach a copy of the notice and lease to each copy of the Complaint.
The filing fee is different depending on where you live. After the Complaint is filed the Clerk will issue a Summons. A copy of the Complaint, Seven-Day notice, and lease may be attached for service on the tenant. The clerk will usually offer to arrange for a Deputy Sheriff or a process server for you. If you are doing the serving, you can post the Summons on the Front Door of the property.
The court will notify all parties of the Court Date, usually the earliest possible court date is seven days from from filing, but the average wait will be ten days to two weeks. District court calendars assign certain days to deal with each type of proceeding. Make sure you have all of the monies owed calculated for your day in court; rents' due, late fees, court costs, etc.
Many tenants will not show up for an eviction court date. Some will have moved before the date, many others believe that the outcome is inevitable; either come up with the money or move. If the tenant fails to answer the Summons and show up in court, the landlord may request a Default judgment. The judge will usually grant it.
If the tenant does show up in court, the judge may ask you to state your case and the tenant will be allowed to answer. Provided the proceeding remains confined to a failure to pay rent, the judge will likely proceed with a judgment for rent and possession. The judge may even ask you to arbitrate to work out a payment plan.
That's a quick summary, theres a bit more to it than that, but that should help.