Head cross-country for a mile or so to the base of the mountain. The mountain is obvious. You’ll be looking up at the northwest face.
Although the upper portion of the mountain is essentially cliffy, you’ll notice a steep, but apparent, weakness on the northwest face. Options from here are plentiful.
Working this weakness directly, you’ll note that it’s not as steep as it had appeared from below, and that it forms into a sort of gully as you ascend. You can follow this weakness class 2+ to a shallow saddle between the summit (to the left) and something resembling a sub-peak (to the right). From there, follow your nose class 2 to the summit.
Although impossible to describe in any real detail, you can alternately head up along the more strenuous terrain to the right of the weakness, following any line that looks tempting. Taking this path, it’s unlikely you’ll find a way up easier than 3rd class, though I can confirm that it can be done at 4th class. As stated earlier, part of the fun of Hart Peak’s northwest face is route-finding your way through the various obstacles along the way.
Just have fun and pick your own way.
Only the most basic of desert hiking gear, unless you’re looking to do some technical routes. To my knowledge, none have been put up.