Want Roommate Evicted, How Do I Start

My question involves an eviction in the state of: Texas
I want my roommate to move out. I've verbally told her 3 months ago I wanted her to move out and she has made no attempt to do so.
The lease is in my name and my roommate moved in about a year ago, and pays half of all the bills.
The landlord agreed for my roommate to stay and I asked my landlord if I can have my roommate move out and my landlord agreed.
It's been 3 months and I do not want to live with my roommate any more.
I'm going to sign a 'renting together' contract with my roommate for court purposes later, if necessary.

If my roommate is late one day on rent can I begin the process of eviction?
Will I have to go through the courts to have my roommate evicted?
If I can provide proof my roommate is crazy can that person be evicted on those grounds?

How are you going to prove your roommate is "crazy"?

To begin eviction process, there has to be reasons for it, such as late payment of rate, failure to pay rent.

Basically, you need to look up your states laws, pay a filing fee, pay for having the person served. Once served, it is usually 30 days.