Just a couple of quick thoughts -

When I first started riding it took a while for me to get the strength and balance to try standing up (I'm a pretty heavy cyclist, so standing up is much more demanding), and when I finally did, I found that the bike felt squishy and unstable - it kind of freaked me out and I hated it. I'd sit right back down again!

But then two things changed - I got new wheels, which were much stiffer, and I had a professionally bike fit session, after which I felt more balanced and centered on the bike.

Also, I took a cycling skills clinic last fall and it was fantastic - I re-learned how to ride no-handed, among many other drills - like Torrelin mentions - all of which really helped me feel more comfortable and balanced on the bike. If you can find a take a cycling skills clinic anytime soon, I strongly recommend it.

So, while standing is still very tiring, I do feel more comfortable out of the saddle.

On the other hand, I hate standing on the trainer - I feel like I'm going to pitch over forward - I think I need to move the bike underneath me to be able to stand and pedal hard. I suspect it means I need to improve my form when standing. Luckily there is always something new to learn, so we never get bored!