I won't be cute with the steps, or pretend I've mastered it. I've had it work great, and also had a three-patch 'new' tube make me wonder why I ever bought a new one.
For me three or four irons makes it easier. I use two of the shorter cheapies to hold the bead and two longer more expensive ones for prying. I also use soap (soapy water, but more in a moment) instead of powder to lube the rim, and leaving the tire in the sun to warm first helps.
But ... for some reason alloy rims seem to mount easier for me. Last summer I swapped tireas and replaced tubes on more than one of my vintage full sized bikes. Tubing my daughter's XR100 with chromed steel rims was another story! After purchasing two new tubes (three pinches is my limit) and still not getting her 19" front right I went to a local wheel works (that's all they really do --- true wheels, mount tires, etc.). They've been around forever and most of the Denver area shops use them for truing.
I walked in just before the owner locked the door, and talked him into doing the job with stories about my poor thirteen year old having to sit around crying while everyone else rode the next day. Softie that he is, he grabbed a new tube and I followed him back to his laboratory.
For a stand he used a steel drum, like a 55gallon oil drum, but maybe 20 gallons (34" high, two raised ridges around it). His tire irons were impressive --- probably 15" long, with round handles and cupped curves for prying. I experienced iron envy, but don't really think size matters. It's what you do with them.
Removal wasn't an issue, as I brought the wheel with one bead off the rim and sans the tube I'd yanked out and jumped up and down on while cursing a blue streak. He put in a brand new tube and inflated a little air into it to round it some (I've always done that too).
I did pay attention now though, and think I'll do much better myself when I next attempt a mount. Instead of the soapy water I always made a mess and soaked the knees of my jeans with, he stuck his hand in a coffee can and smeared the bead with what he said was special soap they use for mounting truck tires. I think mechanic soap, like Goop, would work exactly the same way. He then used two of the irons I described in much the way the earlier posts described. The real key though, I believe, was that he never brought the handles of the irons beyond vertical when prying the bead on. With the drum as a work stand he pushed more than half on by hand, but then used the irons. I said something about him not going past vertical, and he said he didn't want to pinch the tube. When he finished I asked him if that was the trick, and he said, "You watched me, didn't you?"
I told him how grateful my daughter would be, and that it might even help with her medical condition to raise her spirits, shelled out $16 for the tube and mount, and went home a poorer and wiser man. I've found that combination seems common.