1. Have money. Get training from Faralda. If you do alchemy or enchanting, this is quite easy and natural. You don't actually need money, you just need lots of expensive potions and/or banish enchanted daggers to sell to Faralda. You just need the Merchant perk in Speech. You can also do the Training then Pickpocket the money back if you are so inclined. This is quite easy to do up to level 51.
2. Use Runes. Runes are very Magicka expensive, but they are low level apprentice spells so getting the apprentice perk at destruction level 25 gives you 50% discount. You want to be able to cast Runes as soon as possible. Leveling of destruction depends on the raw magicka cost of the spell. So you want to start using the most expensive spell as early and as much as possible. You want to get and use Firebolt as soon as possible instead of Flames. (Ice Spikes instead of Frost. Lightning instead of Sparks.) This should happen super early even before you have the apprentice destruction perk. Using Firebolt instead of Flames accelerates your XP growth. Using Fire Rune instead of Firebolt accelerates your XP growth more.
Later on you want to start using expert level spells (Incinerate, Icy Spickes and Thunderbolt) to accelerate your XP growth even more.
Invest heavily in Magicka in early game. Get cost reduction gear. Upgrade the gear aggressively. Sometimes you meet difficult to kill enemies, sometimes you meet easy enemies. In battle, try to use as much Magicka as possible without being in dager. Kill deers and foxes with runes, not flames.