Eat in local food joints rather than international-looking food restaurants. A set of dumplings can come at only 2000₮.
Get a SIM card to be always connected. I use Unitel, it works in most of the country. All you need is your passport on the moment of purchase. I usually pay around 15000₮ for 30 days, for 512Mbs of data per day. If you go over this you still have data, but it runs at a slower speed.
Get a travel card to catch buses in UlaanBaatar, instead of trying to get taxis.
If you are joining organised tours, instead of getting a guide that cooks, stock up on food and cook your own meals.
I’d usually say to try and get the local transports rather than joining organised tours, but Mongolia is not the case. Definitely get an organised tour, at least with a good driver, a reliable car (UAZ russian vans are way better than Jeeps and other fancy 4×4’s!), a planned itinerary and if possible, a guide also. You’ll be saving time, and mostly, enjoying the country better… time is money, you know 🙂