The first stage is to 'capture' the textures from the game. Follow the instructions on the Glidos site to capture textures:
http://www.glidos.net/retext.html?lang=en
Note that many of us have already captured complete folders of the first few levels and will be posting them up on my new website coming in the Spring. Capturing complete texture sets with everything in place is very time consuming and tricky if you want to do it 100% correctly. But simply capturing wall and floor textures is easy if you play through an entire level from start to end.
My current site is here:
http://www.resonantedge.com/trx/
The stuff on there is woefully out of date, but shows what's possible. The largest texture you can create is 256x256 so it's not up to modern standards, but it's enough to add extra realism.
Here's some threads on the Vogons Glidos forum that you can have a read of that you might find interesting:
Tomb Raider High Res Texture Project
TRx Texture Feedback
Tomb of Qualopec / JC
Lara home-3
Tomb Raider Xtra as a community effort?
more fingers in the pie
My Take at Cave Textures
PNG Transparency issues in replacement textures
Error in 'Texture Correction' instructions
There's no similar way of increasing texture resolution on the other TR games, but Paul has previously hinted that something similar to Glidos could be used on DirectX games... it doesn't yet exist though!