I think my biggest issue is when I play assassin type characters I tend to focus more on actual fighting (dual wield especially) and less on sneak checks. Dragons are the bane of my existence when it comes to sneak characters, unless I'm using a semi powerful bow.
You definitely need to take advantage of sneak attacks. Some tips:
- Before you shoot, scope out a good place to hide (behind a rock, in the shadows, etc). Then, move a little ways away from it, shoot, and sneak back to your hiding spot. Enemies will look for you in the place you shot from, so try not to hang around there for long, especially if it's somewhere your enemy can get to (e.g. down the hall in a barrow, as opposed to way up on a cliff above an Imperial camp).
- Stay as far away from an enemy as you can when shooting them, because that will give you more time to move and hide without them seeing you.
- Get boots with the Muffle enchantment as soon as you can (guaranteed from the Thieves Guild and Dark Brotherhood, very rare to find randomly in shops). Until then, and while you're building up your sneak skill, sneak veeeeeery slooooooowly when near enemies, as you'll make less noise. You can also take off all of your armor and sneak around naked to make less noise—not a great idea when you might suddenly be attacked by, say, a sabrecat, but to sneak past a single draugr, or for some late-night thieving, this can really help!
I've got to head out, but I'll think of some more tips for you and be back with them later.