How to measure and cut square tiles to make a herringbone pattern?
Travertine Limestone - These are natural stone tiles with a saw cut edge.

I would rent and use a diamond saw tile cutter and use plenty of water during the cut to keep the blade cool and the lime dust down.

It's all in the setup on the saw, make sure you get the sawcut exactly centered, cut in one smooth stroke and make sure the tile is secured so it won't move during the cutting operation.

Otherwise you'll get a funny cut that will be obvious in the final layout.

Travertine and Slate are some of the softest and most easily cuttable natural tile you will work with. Be aware that either can have imperfections and can break away on the edges so have spare material available.