Im playing an archer and have already gotten pretty high level, but notice that destruction enchants dont get very many charges - because my destruction skill is low. So I went to try to skill it up and it seems like it goes up REALLY slow. Any ideas on how to speed it up a little?

If you enchant your equipment with "Fortify Destruction" to get down to zero magicka cost for destruction spells you can keep spamming Rune spells for a while and level things up pretty quickly.

It seems a slow skill to level, I need it at level 70 so I can buy the Fire, Frost and Shock perks so they'll be 50% stronger when I find a Elven Sword of the Blaze or whatever.

I've got it upto level 41 (13 hours on this file) just by playing my Warrior with a sword in one and flames spell (can't really use more powerful fire spells as I don't want put points into magic) in the other. It would be upto 70 by now if I had bought training in Destruction.

So unless there's some easy levelling trick (like blasting Shadowmere with fire spells or something) you might be best just trying to implement some destruction spells into your playstyle.

Shadowmere+Fire rune+fire blast. The splash damage will help set off the rune, and together it's almost if not a bit over 100 damage, real great for power leveling. You'll have to wait for shadowmere to regenerate health (he does it reasonably quickly) or manually heal him after a while.

If he reduces it to zero he'll have infinite uses on his enchanted weapons anyway.

True, but this way he can level up more.

It sounds like he wants to level up destruction in order to get more charges out of his weapon. If the enchanting gives him infinite charges, why level up destruction?

I would have to wear the +destruction enchants all the time but I really like my +archery/sneak set.

Higher-ranked skills get you more experience points, so blasting monsters with Fire Ball is more effective than Flames. It comes at the cost of more Magicka though, so keep your magicka potions ready (if you create these via Alchemy, you can level that too).

If you get destruction to 60, you can get perks to make more powerful enchantments. (50% to damage)