Yazd is a desert city in Iran with 423,006 inhabitants (2006). The city is famous for being in a desert, the mosque, and the little alleys in the city's old town.
To get out of the city, ask any driver to take you to 'gate of the city' (they call it in farsi something like "darvaza"). Most Iranians in cities work as freelance taxi-driver, but they don't charge too much, and you also can use Snap as easy tool to take a taxi without being scammed. Having an offline map of the city will help you very well. You can walk to one of the city gates as well but it will take you a long time - especially when you're in the center of the city. From there, the highway starts and you can start hitchhiking.
South towards Kerman-Bandar Abbas
Try to get to Shohadaye Mehrab square (its quite close to city center) and from there, find the big bus stop. Ask around for the bus to Mehriz (30.000 rial on november 2019; about 0,25$) and get out of the bus in the highway, before the bus turn right to Mehriz. The bus will stop wherever you ask, as usual in Iran. From that point in the highway you can easily find a ride to Kerman or even further south. Oil truck drivers are the best ;)