Depends on your definition of mountaineering. Climbing Denali, or hiking to the top of Whitney? Whichever, start by becoming an experienced backpacker and then start bagging peaks. Maybe do some snow camping. If you’re in college, join their mountaineering club.
If you move to the SLC area you’ll be very close to the Wasatch and Uinta ranges, there are hundreds of peaks there to choose from, and many are within day-trip distance. I’d google to see if there are any SLC-area hiking or mountaineering clubs that are doing group trips - some may be able to loan out gear like boots or crampons if you don’t have them. Good luck out there!