How do I evict a tenant that has not paid rent in several months? What can I do to collect the rent that is owed?

Evictions laws vary by state and are a formal process of filings and court. Start by calling your city hall clerk or county courthouse clerk. They usually know where to refer everyone. Suing for past rents can be done in small claims, but even if you win, you may never be paid. That's why it's good to have deposits and to not let rents slide.

Why have you waited several months? Generally the process goes like this when the tenant fails to pay:
First you give them a pay or quit notice giving them 3-10 days (depending on local laws) to pay or vacate.
If they do neither you file with the local court for an eviction order. A hearing is scheduled, and the result is usually an eviction order.
If they still don't vacate you hire a sheriff to physically remove them.
Finally you sue them for what they owe, but if they won't pay the rent, good luck in collecting on a suit.