A good way is by using a portable streamer. There are many such units available online. Take care not to burn yourself. Once you've removed your stains consider sealing your tile.
Well to remove a water stain from the travertine tile you have to use some vinegar. Use the vinegar to remove the stain. Leave it on for a while and then scrub it off.
If your travertine tile is polished and water stains are dull marks then it will be surface damage
created by acidic substances. To remove such a type of stains you should buy good quality marble repair kit. If your tile is hone finished and the water stain is darker then you have to use one sealant to prevent further staining.
It is very easy to clean these type of stones. First we take a old brush and warm water. Then clean the tiles. Next we use the vinegar and apply the stones. Vinegar helps to clean the tiles and clean the small corners with a tooth brush.
In this case it is probably best to replace the tile with new tile. I say this because you may have a water leak behind the tile that is causing the water stain. You'll need to fix this first anyway.