A clean travertine makes a bigger difference than you'd think. Here's the most effective method, plus the mistakes most people make.
Remove all loose dirt and debris. Travertine is porous and can scratch easily.
Use a stone-specific cleaner with warm water. Never use acidic cleaners (vinegar, lemon) on travertine.
Wipe the surface with a soft cloth or sponge. Avoid abrasive scrubbers.
Wipe with a clean damp cloth to remove any cleaner residue.
Apply travertine sealer once a year to protect the porous stone from stains and etching.