As an amendment to a broader bill on education. Details here, from the Austin American-Statesman. Campus carry already passed the House as a stand-alone bill, so it seems likely that the House will concur with the Senate amendment. Texas Governor Rick Perry has repeatedly indicated his support for the measure. The floor discussion of the amendment should be available here, in RealPlayer format (although the Senate site warns that the stream has compatability problems with RealPlayer 14).
If enacted, the bill would only authorize carry by persons who have already been licensed by the State of Texas to carry throughout the state. Permit applications require fingerprinting for the background check, and passing a safety training class. Permits are only issued to persons aged 21 or older. Of course a licensee may not carry a firearm while intoxicated. Texas Penal Code 40.035(d). For a guide to the Texas concealed handgun laws, which in many respects are more restrictive than the handgun carry licensing laws of many other states, see this document from the Texas Department of Public Safety.
For discussion of the policy issues involving campus carry, see my article Pretend ‘Gun-Free’ School Zones: A Deadly Legal Fiction, from the Connecticut Law Review. As the article observes, campus carry has been the rule for years at public colleges and universities in Utah, and at Colorado State University, among others. There have been no reports of problems.