Mages (Karthus, Gragas, Ahri, Brand, or those with good ability power): Start with Doran's ring if you feel like you need extra survivability against your lane or go boots + 3 hp pots with boots if you feel you need that extra movement speed to dodge your opponent's skill shots/you're afraid of early ganks. Never build a Mejais, build Rod of Ages if you can rush it. Standard items on all AP carries are Rabaddon's Deathcap, an Abyssal Sceptor (for Magic resist), Rylai's Crystal Sceptor, Zhonya's Hourglass, or maybe a Will of the Ancients (if you want Spell vamp). Oh, and Flash + Ignite is usually the standard combo for summoner spells. As for runes, they can vary depending on your hero's weaknesses/strengths.
Will be willing to give other tips for other roles or for a specific champion in general if you need help.