Welcome to the forum. Start with what you do know and make a spreadsheet. The try to see if the counties have online datasearch capabilities. You may be able to find some that way. Use the trust name and also the ancestor (or more) that set up the trust. Once you find all that you can find, you might hire a landman that works that area and pay them to do the footwork in the counties that are not digital yet.
https://www.ogm.utah.gov/ Learn what the state rules are, where wells are, resources, etc.
Get to know the business. Read the Mineral Tab above. Also read all the posts for the Utah Mineral Rights area. Not too much activity, but will get you started.
I find this website helpful. Go to the Search Documents tab and then LSR. You can type in the Township and Range and get maps. I start with the Master Title Plat. These are the original patent maps back to statehood.
http://www.glorecords.blm.gov/search/default.aspx
