I'm not a big gamer, but I've enjoyed Oblivion and Skyrim. I've always played either a fighter or an archer. I was thinking of creating a Skyrim character that was a magic user and was wondering if there are any basic tips. One question to start, I notice that I pick up a lot of magic robes throughout the game. I gather that means that magic users don't usually use armor. What's the best method of defense then?

Use alteration spells that boost armour rating e.g oakflesh. And use the alteration perk mage armor to boost those spells that I mentioned while wearing robes. Use conjuration to summon allies and a follower (melee) to keep the heat off you. You can all so use illusion to make enemies fight each other or to calm them so they don't attack you.

Alteration has a set of spells which work as an armour over your robes, while Restoration has a set of spells which work as shields. The former spells remain active for a limited period of time, while the latter ones last as long as you keep the key pressed, and consume quite some power. My advice is, even if you want to play as a pure sorcerer, do not rely exclusively on robes, especially if it is your first time.

I don't bother with Alteration, but it does have it's pluses. I always play a Mage that wears a mix of armors and clothing. It comes down to what looks best. If you are interested in the most powerful combination, invest time and perks in Conjuration and Illusion. Those two schools are all you need. If not for enchantments, you could actually play this character totally naked on any difficulty, because you never get hit

I have only taken up restoration with one character. A spellsword that was a holy smiter. Otherwise, I always had other interests.

Alchemy just makes life easier. Restore magicka and fortify destruction are no-brainers.
If you are unarmoured, do not get into melee ever, or that bandit chief will one-shot you, with a finishing move to rub it in.
Wards can be very useful against dragon breath.
Oddly enough, if you use destruction a lot then another mage, or an archer, might make better companions than a melee character, simply because you will hit your ally with your spells less.

Use everything to your advantage. Enchanting, so you can get you Destruction cost down to 0% and then maybe heavy armor for a bit of defense.