I put most of my tires on by hand.
I use two long tire irons, a large rubber mallet and plenty of soapy water. WD-40 helps too.
I just did 4 tires on my brother's wire wheel Midget, I did all the tires on my Miata and even the 8-ply 16.5 truck tires on my old StepVan. I'll probably put the snow tires onto the Mazda soon (by hand).
The toughest are the Kumho or Yoko DOT race tires on 13" rims for the the race car....very tough!
I have a portable bead breaker to "unstick" tires. In a pinch, I'll drive the front wheel of a car over a tire and it that will usually break the bead if you do it "just right". The valve core must be out (not just let most of the air out).
When I was 14, my Dad taught me how to do this (on my Austin A-40). I'd say that there's "a knack" to it.......not that hard to do, but hard to explain.
In most cases, you put the tire on via the back of the rim so that they go into the "drop center" easier.
I have a small static balancer that's modified to work well on Sprite wheels, so I'm pretty well all set.