How do I get started on a divorce

Every divorce action begins with the filing of a divorce petition.  This is basically a list of what you are asking the court to do:  grant a divorce, change your name, divide property, set up child support, etc.  If the divorce is agreed to, then the next and final step is to prepare and enter a final decree.  You will need to appear before the judge at a 'prove-up' docket.  This is where you put on about five minutes of testimony setting out that you are requesting the divorce, that the marriage is over, and that you would like the judge to sign the decree.  If your husband signs off on the decree ahead of time, he does not need to be present.
This is a really basic thumbnail sketch... to have a better idea of what forms you will need, call your local district clerk and see if they offer an online form bank that you can tap into.  Larger counties, like Dallas County, have a series of forms online that you can access and fill in the blanks.  (you can use most of the Dallas forms in any county)
The forms now available have been very helpful for people to get inexpensive divorces.  However, I suggest that you at least arrange a consultation with an attorney and have them look over your paperwork before you file it.  They can make sure that you are presenting the paperwork you need to insure the correct things happen in your divorce.  Some will charge you a small consultation fee, but it's still much cheaper than full representation.