It's easier to get a good "bite" with three tire irons:
Once the tire is popped off one side, reach under and pull the other side off the same way. Those curvy tire irons are fantastic! Use lots of Windex for lubrication.
Now it's time to clean the old rubber, wheel weights, bugs and other crap off the wheel so you can properly balance it and provide a good seat for the new tire:
Next chunk, balance the wheel without the tire!