I have a tenant that moved in and then would not sign a lease or pay deposit. The property is far from where I live and I allowed the person to move in on a weekend and then he was suppose to go to a realestate office sign lease and pay deposit. However he has not done so and it has been over a month now. Makes excuse after excuse why he can't pay the deposit. Thus he is in the property with no written lease and I have no deposit. What steps to I have to follow to evict.

What State? It varies from State to State.

He is now renting on a month to month basis and after he destroys your rental, you have no deposit.

So my first thought is what were you thinking, and it is obvious you are not in business doing this. This is why you hire and use a real estate agent to do this, and you don't even get invovled.

So now you give them a 30 day notice ( assuming they have paid rent) to move, and just evict them.

The eviction process varies by location. I could never understand why a person would ask such a question without giving a general area.

As Chuck said, without a written lease he's month to month tenant. Depending on where the rental is you may be able give 30 days notice, or you may have to give one full rental period. If the rental period is a calendar month and its not Jan 3 you may not be able to require he vacate prior to Mar 1.

Now you need to have someone regular check the apartment to see if he hasn't trashed it. You also need to check references or make sure you can go after him if he leaves the place a wreck.