There is no requirement that one have an entity (LLC, corp., etc.) to be a small business in Texas. You can just run your business as a sole proprietorship.
To form an entity (LLC or corporation) you file a certificate of formation with the Texas Secretary of State with the filing fee. You'll need a federal tax id number to open your bank account...most banks want to see the formation docs (certificate, operating agreement, etc.).
I would recommend having a competent CPA help you decide what type of entity is best for you from a tax perspective (which drives most entity selection from my experience) and hire a competent attorney to discuss with you the formation issues and form the entity. When I was in private practice, I charged a flat fee of $900 (including minute book, state filing fees, etc.) to form an entity.
That's a quick outline that didn't cover everything, but hope that helps.