As you noticed, Destruction is pretty straightforward. Each cast and while continued casting, you will increase skill, but this has a caveat: only if you are attacking someone. If you're fizzling your spell in the middle of town, it's not going to increase it.
Alchemy is also straightforward: each potion created will increase your skill. As dpatchery notes, eating ingredients for effect determination will also increase your skill by a small amount.
With Enchanting, each enchant (or disenchant, as LessPop_MoreFizz notes) as will increase skill. dpatchery also notes that you can increase your skill by recharging items with soul gems.
Restoration, namely the healing spells, only increase skill if your health is below its maximum. The others only work if you're in combat or near hostile enemies: this includes spells like Steadfast Ward.
For summoning spells (essentially most things in the Conjuration school), you won't get a skill up for the summon until you enter the range of hostile mobs and, in the case of summoned creatures (like the Atronach and the Familiar), they do some damage. With bound weapons, entering range of hostile mobs is all that's necessary to gain Conjuration skill; however, using them in combat will increase their appropriate weapon skill, not Conjuration.
Alteration and Illusion spells that are targeted towards messing with hostile mobs need hostile mobs within range to skill up. Buffs, like Oakflesh, don't increase skill without hostility as well. Others, like Candlelight and Muffle, are recastable without hostility but only increase skill by a small amount.
Dwarven Oil and Taproot have the exact same effects: Weakness to Magic, Fortify Illusion, Regenerate Magic, and Restore Magicka.
If you create a potion from these ingredients, it would have all four effects (3 positive, 1 negative). With the Purity perk, the negative effect would not appear. As a potion, you can drink it.
If you create a poison from these ingredients, it would have all four effects (3 positive, 1 negative). With the Purity perk, the 3 positive effects would not appear. As a poison, you can put it on your weapon.
Best Answer
Thankfully, Skyrim does not suffer like Oblivion from all those unintuitive effects.
The one exception is magic ABSORB (not resist). It is available from the Breton's activated racial ability, the Atronach standing stone, and an Alteration perk. Even then, it only causes your conjurations to fail, and does not affect your healing magic, potions, etc. My Breton character simply doesn't conjure anything and enjoys full effect from everything while laughing off mage NPCs. If you want to conjure things and resist magic, simply avoid magic absorb and steer yourself towards hitting the 80% RESIST magic cap.