I have tried casting flesh spells, and even with the reduction perks in alteration, I don't have enough left over to use my attack (destruction) effectively.

I am levelling enchanting, but in the mean time, how is that done?

Hmm.. what level are you, and how much max mana do you have?

With all my mages, i always cast the flesh spells right before a battle too, and dont use too much mana,

Are you also wearing good mage gear? Like robes, hood/circlet, amulets and all that? I usually make sure most of my equipment is mana increasing gear.
Also, the two perks in restoration that add mana regeneration, they help a lot too.

And if you're someone that is willing to sacrifice body for more power, then the apprentice standing stone is nice for that extra 100% mana regeneration. Of course, you really have to watch for spells and use wards a lot to defend against it. (ive got a mage to level 40~ on master difficulty using the apprentice birthsign the whole time, and its not too hard)

I havent had too much troubles on mages running out of magicka before, but i also put every single level into magicka and nothing else. So by level 35-40 ill have 100 hp, 100 stamina and 750 mana.

Also, being a high elf really helps. The highborn ability basically gives you unlimited mana for 60 seconds.

The perks will only half the magicka cost of the spell, so the first few levels of a new spell will be tough to cast until you get more magicka. Even if you have apprentice level spells, you may still want to try a novice mage-shield spell with an apprentice level destruction spell.

Another tip is to cast mage shield and conjure pets before battles take place. I know this is not always possible, but it helps if you are already buffed with a full mana bar before the fight.

Eventually when you reach high level enchanting, you can reduce the spell cost further to the point where it is mana free to cast a school of magic, or you can reduce the cost of several different schools of magic to the point where it is almost mana free. I prefer the latter, where I have reduce the mana cost for conjuration, alteration & destruction greatly, but not completely mana free.

I go for a 3:1 magicka/health ratio with cost reductions and that seems to work ok.