I'm in a guild now and have a lot of friends, but that didn't happen until after level 40 or so, so I solo'd my mage for a good part of the time, besides being in PUGs for instances. Wasn't really that hard, and I'm saying this as a noob who'd played a lock for a short time before-hand, and hadn't really played any other mmorpgs, besides runescape, which hardly counts. I'm in Outland now, and I'm kind of whiny about soloing out there, but, until now, I've never really had a problem. And I don't really have a -problem- now, it's just that it's ugly in Outland, and fire spooks me and it's everywhere, plus I have guildies to whine to. :) I could do fine solo if I wanted, though, just a pita.
The best thing to do is to train every time you can and start adding all the spells to your bar, and learning to use them in different situations. I like the way the very beginning is for mages, because a couple of the quests tell you exactly which spells to use to complete the quest. I don't think I ever would have used mana tap otherwise. (not that I use it now. :) )
And...well, attack from the farthest distance you can. :)
And read these forums. Lots of awesome info you can pick up everywhere!
Good luck,
Trill