Yeah, just takes time - after a few weeks it will just take you a few seconds and you'll wonder how it was ever so hard.
I teach people regularly how to do it (and my way is right!) and I average about 1 1/2 appointments - of 20 mins each. If you get to 20 mins it's worth quitting as you just get frustrated and have sore eyes.
Same goes for taking them out - don't leave it until 11:30 at first - start at 9 or something so if you can't get them out go and do something else for 20 mins and try again.
No use panicking about it.
and had at least one night where I thought I'd be off to A&E because I couldn't get the lens out again!
If you're really stuck it's unlikely you'll do any harm leaving them for 1 night and getting help in the morning - and I would suggest A&E is not the place to go - the docs have very little eye training and contact lens removal isn't taught even if they do.
Just leave them and speak to your optician in the morning.
Many of the new high oxygen lenses are safe for occasional overnight wear - but even if it's a regular lens 1 night shouldn't cause any problems if they're well fitted.
My number's on my office answering maching but I've never had to get out of bed yet!