How can I keep a DWI off of my record?

Possibly.  Since you didn't give more details, it's hard to say.  However depending on the facts of your case it can be done in several ways.

If you case was dismissed, you can have your record expunged.  Once expunged, the release, dissemination or use of expunged records by any agency is prohibited.  Unless being questioned under oath, you may also deny the occurrence of the arrest and expunction order.

If you received deferred adjudication of a class "C" misdemeanor in Texas and you completed community supervision, you may be eligible to have your conviction "expunged".  The release, dissemination or use of expunged records by any agency is prohibited.  Unless being questioned under oath, you may also deny the occurrence of the arrest and expunction order.

 If you were convicted in Texas and successfully completed probation, you may qualify to have your conviction set aside and to have the case dismissed. The Texas Code of Criminal Procedure gives judges the right to dismiss a case against a convicted defendant who fully completes the terms of his or her probation. 

If you have completed deferred adjudication (as opposed to being convicted) and the statutory waiting period for your offense has passed, you may be eligible for an "Order of Non-Disclosure". This order prohibits the government from disclosing your criminal conviction to the public.  You may then legally and truthfully deny your conviction.

Your juvenile record may be available to law enforcement, educational institutions, licensing agencies, and even employers. Sealing prevents anyone from accessing your juvenile records except in criminal proceedings. You may be eligible for sealing if two years have passed since discharge and you have not committed a felony or a misdemeanor involving moral turpitude since then.

 NOTE:  If you were convicted and served time in state prison, your only option is a pardon from the Texas governor.