General Nid Tips
Decide if you want to play AD or AP Nid and choose your runes and masteries accordingly. Stay away from hybrid Nid for now if you're a beginner to her mechanics.
Use traps often. The damage seems small but it's a mana effective way of dwindling down enemy health. Also make sure to poke and attack after trap damage whenever possible, the armor/mr reduc adds up.
Maintain bush control. With traps, wards, spears, auto attacks, ganks, I don't care. Bushes protect you from ganks and give you the speeds. Get it.
Last hit with auto attacks. Clear mobs with cougar.
Learn to use abilities while moving. Nid is all about mobility.
AD Nid
Size up who you're up against. Some enemies can be damaged with hard harass. Others need to be kited and poked. You won't do much killing till level 6 so focus on last hitting. Any time an enemy champ is >40% hp you can go for the kill in cougar form with W, E, Q in that order. Also, don't bother maxing out your spear first, it's a waste of mana. Heal and traps are much better.
Tank Nid is also an option, just make sure you get a sheen with it.
AP Nid
Max out dat spear first for teh damages but don't fire it unless you have a clear shot. It costs alot more mana than you'd think.
Deathcap before Lich Bane. Rushing Lich Bane forces you into close range combat too much for insignificant damage boosts. Bad for AP Nids who need to kite with spears.
After chucking a spear, R into cougar and hop away for additional distance damage boosts.
Spear, cougar and hop, while running. When they are low you can turn around for the kill.