What is the best way to increase your destruction in Skyrim?

Answer 1

Fire spells do the same damage as the lightning and ice spells, yet costs less Magicka. It also keeps burning, doing more damage over time. If you're referring to the Augment elemental perks, I usually do Flames first. Shock is also effective against other magic users, and Dragons. Lightning Bolt, and similar spells are Hit Scan weapons, which means they strike instantly, so you don't have to lead the target. Also, no dragons are Shock resistant.

Each element has it's own advantages, so a good mage knows what to use when. There's a variety of spell effects too, just in Destruction. Ice Storm is probably the best frost based spell, and the best AOE Adept level spell because it travels in a line with a wide area. This allows you to sweep the battlefield, rather than just blasting a small area like Fireball, or strikind a random secondary target like Chain Lightning.

Answer 2

Cast destruction spells at valid targets, the higher level spell you cast the faster your skill level will rise.