How do you fellow mage players go about combat? It seems as if I always run out of mana and have to run in circles until I can do some damage again.

Im nearly full mage (Destruction, restoration, alteration, conjuration main skills) but I also use a 1 handed weapon thrown in the mix a lot. A good 1 handed weapon in my right hand and magic on my left has been working really well for me so far. I also dual cast a lot too. Im almost level 20 and have been playing mostly on Expert.

Edit: I havent put any perk points into 1 handed and I still feel it does respectable damage. Especially if you get a magic weapon that does flame damage for example. Set the enemy on fire with magic and then hit him with your weapon for extra fire damage.

Get some buffs for lydia, summon/or make a zombie for a second meatshield, if you are about to run out of mana summon a bow and use that for a while. Also save, I'm not kidding you will have moment where you walk into a room and get 1 hit KO by a random mage.

I'm playing on expert and I think mages are soooooo over-powered. I can basically one-shot anything with dual fire balls and dragons are laughably easy to kill.

I did complete the mages guild quests though, so I've got some great mage items (mask of Molokai for the win!!!!!!). I also keep a follower with me and use conjuration to distract the enemy if I ever need to recharge. The only enemies I have problems with are the dragon priests and draugr that summon frost minions.

I don't want to assume here, but if you're just running into battle head on without planning your attack or preparing yourself first, then you will die. If you're not willing to do that, then being a mage is not for you. Usually cast a alteration spell on yourself before battle with a serious enemy and adapt your spells to the enemy at hand.
If you're still having trouble, do the mages guild questline, that'll help you.

This. That is for warriors in heavy armor and weapons like myself. Mages have to think about how to do something before going in. Those rune spells look like landmines from Fallout to me, so those may help.

they are definatly for setting before combat. they have really low dmg to mana cost, and can blow you up if your too close when the enemy steps on them. that isnt fair, fireballs dont damage you, fire wall doesnt, why should these?

That's the gist of mages right now. Just stack up on +mana/+mana regen items and guzzle potions. Don't neglect your staff weapons or conjured creatures either.

Landmines (and explosives in general) did damage to both the player and enemies in Fallout, so I guess it is the same principle.

As the other posters have said, mages need a more tactical style of play than previous games. And a good stock of magicka potions. Conjuration is a good thing to have as a fallback. Summon an atronach
if you need breathing room. 132 magicka roughly, so may be an item that can summon one is the way to go. Illusion is pretty cool too. Use spells to get your enemies killing each other while you recharge. Also carry a few scrolls for those nasty moments.

fireball. explosive. -> missile launcher. explosive. your comparison does not work.

Sneaking landmines into raider's pants, then get out of the blast radius. Heaps of fun.

Well if want feel free to tell the devs or mod it out. Just learn to get out of THAT particular blast radious

I haven't played a full mage yet, but I think it might help to conjure up some ghost weapons.

I use a bow for a sneak attack, and then all Magic. I don't understand why everyone thinks mages are so weak. I always set a rune up in advance and then use fire bolt. I can usually kill most things, except for other magic users. (I don't have any conjuration moves and I am level 17)

My save game says play time is 33 hours. Level 31 Nord warrior clad armored in fully upgraded daedric armor and wielding daedric mace and molag bal's mace in dual wield and cutting through giants and mammoth's like grass.
Just completed Companions questline, have'nt touched main story beyond meeting the graybeards and have'nt even joined dark brotherhood and thieves guild yet. So much content and too much things to do