You should read up on Chapter 59 of the Texas Statutes here:
http://www.statutes.legis.state.tx.us/Docs/PR/htm/PR.59.htmMost notably sections 59.042, 59.045, & 59.046 seem to answer your question.
You MUST make a public notice, it MUST be a public auction, and finally, you MUST turn over any excess funds to the tenant (see conditions below).
Sec. 59.042. PROCEDURE FOR SEIZURE AND SALE. (a) A lessor who wishes to enforce a contractual landlord's lien by seizing and selling or otherwise disposing of the property to which it is attached must deliver written notice of the claim to the tenant.
(b) If the tenant fails to satisfy the claim on or before the 14th day after the date the notice is delivered, the lessor must publish or post notices advertising the sale as provided by this subchapter.
(c) If notice is by publication, the lessor may not sell the property until the 15th day after the date the notice is first published. If notice is by posting, the lessor may sell the property after the 10th day after the date the notices are posted.
Acts 1983, 68th Leg., p. 3576, ch. 576, Sec. 1, eff. Jan. 1, 1984. Amended by Acts 1984, 68th Leg., 2nd C.S., ch. 18, Sec. 5, eff. Oct. 2, 1984; Acts 1985, 69th Leg., ch. 117, Sec. 12(d), eff. Sept. 1, 1985.
Amended by:
Acts 2011, 82nd Leg., R.S., Ch. 405 (S.B. 690), Sec. 4, eff. January 1, 2012.
Sec. 59.045. CONDUCT OF SALE. A sale under this subchapter must be a public sale at the self-service storage facility or a reasonably near public place. The lessor must conduct the sale according to the terms specified in the notice advertising the sale and sell the property to the highest bidder.
Acts 1983, 68th Leg., p. 3578, ch. 576, Sec. 1, eff. Jan. 1, 1984.
Sec. 59.046. EXCESS PROCEEDS OF SALE. If the proceeds of a sale under this subchapter are greater than the amount of the lien and the reasonable expenses of the sale, the lessor shall deliver written notice of the excess to the tenant's last known address as stated in the rental agreement or in a written notice from the tenant to the lessor furnished after the execution of the rental agreement. The lessor shall retain the excess and deliver it to the tenant if the tenant requests it before two years after the date of the sale. If the tenant does not request the excess before two years after the date of the sale, the lessor owns the excess.
Acts 1983, 68th Leg., p. 3578, ch. 576, Sec. 1, eff. Jan. 1, 1984.