Sealing travertine is not very complicated and if you take your time and clean it properly before you seal it, you shouldn't have any problems.
First, you need to know if there are any topical coatings such as wax or polyurethanes on the travertine, and if there is, it requires a stripping process, that's different than what it is described below.
Clean your travertine thoroughly with a neutral cleaner or if it's badly soiled, you can use an akaline stone cleaner to break down dirt and grease build-up.
Once the travertine surface is clean, dry it with a cotton or microfiber cloth. It's very important the travertine is dry before any sealer is applied. In some cases, if the travertine is more porous, it may need 24 to 72 hours to dry before applying a sealer.
If you're sure the travertine is completely dry, you can apply the sealer evenly using a lamb's wool applicator or any soft cloth. Honed or textured travertine will require more sealer due to it being more porous than a polished travertine.
Not all sealers behave the same and if you're using a water based sealer, it will take longer to dry compared to a solvent based sealer. It's important not to let the sealer puddle up as any unwanted residue can dry up and even stain some stones.
After applying a second coat of sealer, dry buff with either a microfiber or cotton cloth, making sure to remove all excess sealer. You don't want to see any streaks left by the sealer
If you do see streaks left by the sealer, re-activate the sealer with some more sealer, and then buff off.
Try this sealer for all your stone surfaces, including travertine tile and slabs.