Heres a general concept to do it
1). You want to wipe the travertine surface with a damp cloth to remove any dirt or debris out of the imperfections that exist in the material.
2). Start sanding the surface using 400-grit sandpaper in a circular motion, with just enough pressure to remove only the imperfections on top of the surface (you are not trying to remove all the imperfections since they are normally deep into the material). Wipe the travertine surface when you are finished sanding (getting dust out of the imperfections).
3). Re sand the surface a second time with 600-grit sandpaper. This will begin to make the travertine shine a little. Make sure you remove any scuff marks you made with the 400- grit paper on the surface. Again, clean the surface.
4). Re sand another time with 800-grit sandpaper (you can use 1200-grit sandpaper after the 800 grit to make the material very shiny and "slippery". Remember not to apply too much pressure or use rapid strokes with the sandpaper (you do not want to make scratch -gouges ...this needs to be a smooth process). Make sure to clean out all imperfections again.
5). Finally, use a buffing pad to buff the travertine to a glossy shine (you should not use any type of buffing compound on your travertine).
Good luck with the elbow grease!