Malzahar works very well with AD thanks to his Voidlings, they chase enemies, even behind the tower. Malzahar also scales nicely with AP, both stats are good on him.
Cast your Q 3 times in base so that you have a Voidling ready on your next cast.
Push as soon as you can, Malzahar has big poke, waveclear and tower damage.
Take the enemys heal thingy, if he tries to get it, punish him.
Use E on creeps, spam it. You want to get as many Voidlings as possible.
Harass with auto attacks, your range is nice. Poke with E, Use Q defensively or to push.
Don't level up your W at all, it only costs mana that you don't have.
Try to get a kill or win in cs, don't hit the tower when you would receive damage.
Don't forget the heal on your side.
Go back when you have to, stay as long as you can.
Against melees, stay away from the bushes, hit your trinket button to see them and poke them.

Runes:
Against phyiscal damage:
I use cooldown reduction glyphs instead of magic resistance, you get 7,5% CDR which is really nice. I use armor quints, they give you amazing 12,7 armor, cloth armor gives only 2,3 armor more. When using AD quints you get 6,7 AD which is very little.
Against magic damage:
I take armor and magic resistance, you always want to have armor, it reduces the damage from creeps and tower hits, too.

Masteries:
I don't take many points in offense, going 21 in offense doesn't give you much early game, you get percentage stats and you lose tankyness, Malzahar is a sustain+damage champion. Instead of offensive stats I take points in health regen, basic attack damage reduction, flat resistances and the health shield. I also take points in mana regen and recall time reduction, especially the utility part is very important.

Currently I ban:
Nunu: Outsustains me.
Pantheon: Trades very well and blocks every auto attack when played right. When he goes all-in with ignite you might be down to 15% HP quickly so that he can crit you. Really scary IMO.
Caitlyn if not banned.. (just because of ranged damage)
Otherwise I ban either Yasuo, Riven or Lee Sin. Yasuo and Riven have big damage, a shield and even CC, Lee Sin can get a kill on level 1, I never played against one but I'm really scared.