When I had to fight those spiders in the beginning, before I found out you could zoom out to third person view, and even better, shoot stuff dead before it comes near, I looked away and spammed those mouse buttons until the guy I was following (Ralof? Rolaf?) told me to move on.
Another thing is, I'm having a hard time figuring out what quests to do when. I seem to be skipping stuff, or doing it wrong, because I'm not high enough level to be taking on dragons and giants and stuff, but the quests lead me to them.
For instance, the first dragon you kill, to unlock your Shouts, took forever and a few deaths because of my low level and lack of spells and perks. I got the distinct feeling that I had skipped something somewhere, but the game is so nonlinear that I have no idea where to go.
What level were you? I was 7, and had only spent 1 perk point. That dragon doesn't have much health at all, but it's breath attack still hurts. If you turtle it, the guards will eventually shoot it down. When that happened, I continued to needle it with arrows (which you can do from the safety of the tower).
I ended up killing it with my sword, just because I was hoping for a special animation (but no luck).
Until you get some fire resist gear, though, (or <insert other resist>), it might be tough to go toe-to-toe with a dragon without using range. It's really hard to avoid their breath without cover.