There are several methods to cut travertine tiles, including using a tile saw, a wet saw, an angle grinder, or a tile nipper. The method you choose will depend on the tools you have available and the complexity of the cuts you need to make. Here are some steps to guide you through each method:

1. Using a tile saw:

- First, mark the line you want to cut on the tile using a straight edge or a pencil.
- Turn on the tile saw and adjust the fence or guide to the desired width of the cut.
- Hold the tile securely against the fence and slowly push it through the blade, following the marked line.
- Repeat the process for each cut you need to make.

2. Using a wet saw:

- Fill the reservoir of the wet saw with water according to the manufacturers instructions.
- Mark the line you want to cut on the tile using a straight edge or a pencil.
- Turn on the wet saw and adjust the fence or guide to the desired width of the cut.
- Hold the tile securely against the fence and slowly push it through the blade, following the marked line.
- The water will help cool and lubricate the blade while cutting.

3. Using an angle grinder:

- Wear safety goggles and a dust mask before starting.
- Mark the line you want to cut on the tile using a straight edge or a pencil.
- Turn on the angle grinder and slowly start to cut into the tile along the marked line.
- Use light, even pressure and move the grinder in a back-and-forth motion.
- Keep the blade parallel to the tile surface to ensure a straight cut.
- Repeat the process for each cut you need to make.

4. Using a tile nipper:

- Mark the line you want to cut on the tile using a straight edge or a pencil.
- Hold the tile in one hand and the tile nipper in the other.
- Position the tile nipper over the marked line and squeeze the handles together to break off a small piece of the tile.
- Continue breaking small pieces along the marked line until you have made the desired cut.
- Use a tile file or sandpaper to smooth out any rough edges.

Note: Always wear protective gear when cutting tiles and be careful not to damage the surface while cutting.