hey,
this is my first build, i hope to help a lot of new malzahar players, just becouse malzahar is fun to play.
feel free to comment.

greater Marks of insight: destroy your enemy's magic defense.
greater Seals of force: these are for more late game AP
greater Glyphs of Celerity: no mana regen becouse your malefic visions regenerates your mana, so cooldown for better spam of your spells.
greater Quintessence of potency: just to have some early game AP.

21-0-7
regular AP carry masteries.
this masteries include: cooldown reduction, ability power, magic penetration, increased damage, ability power per lvl, more damage to low hp enemy's, mana regeneration, mana per lvl & buff's for your summoner spells.

the Dorans Ring: hp for more sustainability early game, some AP & mana regen.
Sorcerer's Shoes: of course the movement speed and the magic penetration.
Archangel's Staff: the mana, mana regen, late game mana & lots of AP (about 800AP with full build)
Will of the Ancients: really important item, this item grants you massive spellvamp in combination with your lots of AP, it makes your ultimate a combination between warwicks Infinite Duress & fiddlesticks drain.
Rabadon's Deathcap: massive AP.
Archangel's staff 2x: just for lots of AP. (you can change it for hp items to increase your durability).
on top of this guide it says u should have 386.05 AP at lvl 18, but this is without the extra mana & AP from the Archangel's staffs.

max malefic visions as fast as possible, this is your main harras spell.
after that max call of the viod, just to do some more harras damage.
at last max null zone, to increase your full combo damage.
choose nether grasp at lvl: 6, 11 & 16.

your main spell combination should be:
1st: call of the void.
2nd: malefic visions.
3rd: null zone.
last: use nether grasp (while the enemy stands in null zone to max null zone's damage).

ignite: this can be used while channelling nether grasp. (be carefull, if you are out of range while using ignite, nether grasp stops channelling and so your ultimate is wasted.) ignite is really usefull to do the last bit of damage to finish someone off.
flash: this could be handy when chasing someone, but becouse you dont have a lot of hp & no escape ability, flash could be coming very handy.

try not to jump into groups of enemy's or plat to aggressive, instead, stay a bit behind your team & use your spells to focus one enemy with your team.
this is a build that works best for 1v1 malzahar. so in teamfights, look out and be carefull.

have fun with playing malzahar.