Fall is the best time to do this. But since your foundation work is ready to be started, I guess you have to get going now.

First determine the location to where the plant is to be moved. Then dig a hole at least 18 inches in diameter and two feet deep at that location. Amend the hole with compost etc. Then hard prune the plant leaving only about 24 inches of the vine. Start digging a good eighteen inches from the crown. You will have to dig about 2 feet deep as well. Without breaking too many roots etc. pull the plant out and then transfer to the new location. Keep it watered and make sure it doesn't get dried out in the Texas summer.

Depending on how old & healthy the plant is, the root ball could be enormous. So keep that in mind when you start to dig. Goodluck with the move!

aluvaboy gives good advice - prepare the new hole ahead to time, dig as large a root ball as possible, water it in well, and give it a layer of mulch and don't let it dry out (but also don't drown it) for the rest of the season. A few folks have mentioned that they found they could divide clematis when they had to move them, that there were by then several hunks which separated easily (not needing to be hacked apart.) I dug up a couple of somewhat smaller ones this year and potted them up, and if needed for your large plant, a half whiskey barrel or something of similar size would work. In TX in a container, I would most likely give it some shade as well.