Depending on the type of stain and depending on whether or not your travertine had been sealed and polished prior to receiving the stain, stains can be difficult to almost impossible to remove from travertine. The problem is that travertine is a very porous stone. It soaks up stains like a sponge and the stains can go relatively deep down into the stone--depending on whether the stone has been sealed or not. This means that for some stains the only way to get them out is to "sand" down the stone until you have removed the stained portions of stone. This is often done using an abrasive polishing compound or steel wool. For some stains, however, there is a simpler solution.
Clean the stained area with warm water and a mild dish soap. Sponge the soap and warm water onto the stain and allow it to soak into the stain for two minutes. Wipe with a sponge dipped in plain water. Blot the area with a clean cotton cloth, putting plenty of pressure on the stain.
Apply a commercially-available cleaner especially designed for travertine. Such cleaners are available at most home improvement stores and at any store which sells stone products. Follow the manufacturer's instructions exactly.
Pour hydrogen peroxide onto the stain and cover it with a piece of plastic wrap. Tape the edges of the plastic wrap with duct tape to keep the hydrogen peroxide in place. Allow the hydrogen peroxide to work on the stain for half an hour. Remove the tape and plastic wrap and sponge off the hydrogen peroxide with plain water. Blot the stain with a clean dry cotton cloth, putting pressure on the stain so that it will soak into the cloth.
Use 00-grit steel wool if the stain still remains. This is going to take time. Be patient and just keep rubbing the stain with the steel wool. The idea is to take off tiny layers of stone until you have remove the last stained layer.
Pour a half-dollar-sized dollop of stone polish onto the stained area and use a car buffer running at low speed to buff the area. Again, the idea is to remove layers of stone until the final stained layer is removed. Use only moderate pressure on the buffer and be patient. Depending on how deep the stain is, this could take some time.