Gotta have the opposite side of the tire down in the dish of the rim (where the spokes connect). Also review Neduro's Tire Changing Tutorial.
Opposite side of the tire needs to be flush with the center of the rim like mentioned above. Use lube. I use dish soap and water. Heat up the tire in the sun if possible. Wear gloves. I always tear up my hands. Don't give up.
Lube, more lube (that's what my wife says....), take little bites with the tire irons, and keep the opposite side deep in the well. Did I mention more lube????
One more thing. I put the rear tire on with the disk side up if I don't have a wheel stand available. I worry about warping the disk. Glad you got it on there.
After a couple years in Latin America I got accustomed to paying people to put my tires on for me. I recently mounted my rear tire for the first time in a few years and it was way easier than I recall, I must be learning something. For me I tried to focus on keeping the tire within the bead as I was spooning it on. I did this one on the ground but I prefer a good barrel for changing tires.
Use small blocks of wood on the opposite side to keep the wheel in the dish of the rim, I travel with about 4-6 small derlin blocks I used for just that purpose makes changing the wheels much much easier.
I was pulling every trick I could come up with ...pushing it into the dish on the opposite side did it with little effort.