Tire mounting difficulty can vary widely, depending on what tire / rim combo you are working with. The tips about pushing the bead shelf into the center of the rim are good. Here's a video that demonstrates it; the guy in the video is mounting a Marathon Plus tire (sidewall is super thick Kevlar, tough as a car tire) with his bare hands:
https://www.youtube.com/watch?v=-XUFVrl0UT4 Using these tips (sans the bungee strap), I recently mounted tires on 4 HED C2-plus rims and 2 HED C2 (non-plus) rims with no issues. Tires were Compass Bicycles' 700x38 (for the C2-plus) and 700x28 (C2 non-plus).
However, I tried the same techniques using the same tires on my Dura Ace C50 wheels and they absolutely would not mount at all. I probably spent an hour wrestling with it. So I resorted to using the Kool Stop Tire Bead Jack. The C50s are my race wheels and if I ever have to change a flat in a race I am totally screwed, so I sawed off 2 inches from the end of a Kool Stop Tire Bead Jack so that I can store it in my saddle bag.