1

for bus http://www.payaneh.ir/fa/crs.php , choose departure and destination, buying can be done by iranian bank cards
for train raja.ir, i uploaded a link to pdf file including timetables and prices
both in farsi

2

Take the bus. Train is more comfortable but they are not frequent and often full, so you have to book in advance. You can do this at many travel agents in Teheran.

The bus is easy. Go to Terminal Jonub (south terminal) and head for the big round building. In there you will find buses going to Kashan at least every hour, and very cheap.

Outside of Teheran every town is different but the main thing is to find the bus station, which is often out of town. Find out the name of the "terminal" and where to catch the shared taxi to get there. Once you are there you just have to ask someone and they will put you on the right bus. Its normally very efficient.