Hi! This is my build for playing Malzahar, I'm trying to improve it so I will be appreciate for every comment and hints. I hope that you will understand my english :P
Malzahar is powerfull mage with potency to do sick dot's. He can easily take another Champion 1on1 when have his ult ready to use. Unfortunately he's not very quick and he's very squishy so when you play with Malzy you need to look out to not get gank. When there is such possibility take the middle, he is great harasser with his Call of Void and Malefic Visions.
In early game playing with him is very hard because his abilities aren't cheap :) You just can't spam them or you need to get some magic potions. When you get lvl 2 Malefic Visions mana problem is no more :D You just cast it on a mob and target it with your attack and sometimes use Call of Void, Malefic Visions will jump from mob to mob granting you mana :) It's great that your voidlings attack mob/character with MV on it. Try to always have a voidling with you he is great support.
At late game when you have more ability power you can just cast Call of Void to kill entire minions wave. When fighting with Baron always cast Null Zone first the second can be Call of Void or Malefic Visions, when fighting creeps in jungle Call of Void should do the trick if not just cast Malefic Visions on them to finish them of :)
When team fight try to stand back because you surely be the first one who will be targeted :)

Pros:
+ Very high dmg
+ Can silence multiple enemies at once
+ Great farmer
+ Usefull in killing tanks
+ Great for mid control

Cons:
- Squishy
- No escape ability
- Can be gank very easily
- In team fights he is first target

I recommend runes that gives you ability power, magic penetration and of course ability cooldown. I use this set of runes:

Greater Mark of Insight - penetrating enemy's magic resistance is always a good thing :)

Greater Seal of Force - bonus ability power to do more dmg with your skills.

Greater Glyph of Celerity - to use your skills faster and get your voidlings pretty easily.

Greater Quintessence of Force - like with seal of force to do greater dmg with your skills.

Doran's ring: +100 Health +4 Mana Regen per 5 sec +15 Ability Power

Tear of the Goddess: +350 Mana +7 Mana Regen per 5 sec UNIQUE Passive: Each time your Champion uses an Ability their Maximum Mana will increase by 4 Mana, up to a maximum of twice in a six second period; bonuses cap at +1000 Mana.

Rabadon's Deathcap: +155 Ability Power UNIQUE Passive: Increases Ability Power by 30%

Archangel's Staff: +400 Mana +25 Mana Regen per 5 sec +45 Ability Power Passive: 3% of your Max Mana is converted to Ability Power. UNIQUE Passive: Each time your Champion uses an Ability their Maximum Mana will increase by 4 Mana. This effect has a 3 second cooldown. Bonus caps at 1000 mana.

Void Staff: +70 Ability Power UNIQUE Passive: +40% Magic Penetration

Rylai's Crystal Scepter: +500 Health +80 Ability Power UNIQUE Passive: Dealing spell damage slows the target's Movement Speed by 35% for 1.5 seconds (15% for multi-target and damage-over-time spells).

Zhonya's Hourglass: +100 Ability Power +50 Armor UNIQUE Active: Places your champion into Stasis for 2 seconds, rendering you invulnerable and untargetable but unable to take any actions. 90 second cooldown.

Quicksilver Sash: +48 Magic Resistance Active: Removes all debuffs from your character. 105 second cooldown.

Banshee's Veil: +375 Health +375 Mana +50 Magic Resist UNIQUE Passive: Blocks one negative spell every 30 seconds.

As I already told in introduction Malzy have mana problem in early game so Doran's ring should be the first thing to buy, it will give you mana regen with extra hp and ability power. The next item should be Tear of the Goddess it will give you bonus mana, mana regen and cool passive so you could spam your abilities to get Voidlings. After you get this you must buy Rabadon's Deathcap I think it's the best item for mage. Next you should upgrade your Tear of the Goddess to Archangel's Staff to get another passive of ability power :) Void Staff is the next must item because of it's magic penetration ability. Rylais Crystal Scepter is usefull item because of it's ability to slow down enemies by 30% but for Malzahar it's only 15% though (because all his abilities are dot's or aoe). Then buy Zhonya's Hourglass because of it's armor bonus, AP and active ability. Next just change Doran's ring with Rabadon's Deathcap or if you have trouble surviving you can buy Quicksilver Sash which active is like Cleanse or Banshee's Veil which will protect you from time to time :P

I use Exhaust to lower attack dmg and speed so he doesn't beat Malzy that much and (from masteries) reduce target magic defence so we could deal greater dmg for 3s and Ghost in case I need to run away really quick or chase running away enemy :)

I also can recommend these summoner spells:
Heal - it can be usefull because Malzy is squishy.
Teleport - usefull to get back to acion.
Cleanse - usefull because of removing silence, stun and slow:)
Fortify - usefull skill but if someone of the team has it don't take it.
Clairvoyance - usefull when want to find out if enemy team is killing the baron and gank him (as fortify if one of the team has it is useless).
Flash - good skill but in my opinion ghost is better for running away and chasing.

Not recommend those spells:
Clarity - usefull in early game but with Archangel's Staff it gets useless in mid and late game.
Revive - what the hell is this ****? It the worst summoner spell.
Smite - hmm I don't use that one but I think there are better summoner spells than this one.
Rally - I think it's useless spell for mage.

Summon Voidling: Don't underestimate Voidlings! They are great for farming, harrasing and finishing off retreating enemy champions, they are fast and deals fairly good dmg :). If you spam spells you can get two Voidlings at the time (never seen 3 :P). Voidlings have 200 + 50 x lvl Health and 20 + 5 x lvl Damage. Voidlings grow after 7 seconds (+50% Damage/Armor), and Frenzy after 14 seconds (+100% Attack Speed). Voidlings attack the target affected by Malzahar's most recently cast Malefic Visions.

Call of Void: Does dmg to every enemy in the line it can be used to attack enemies behind the wall
Cost: 80 / 90 / 100 / 110 / 120 Mana
Magic Damage: 80 / 135 / 190 / 245 / 300 (+0.8 per ability power)
Silence for: 1.4 / 1.8 / 2.2 / 2.6 / 3 seconds

Null zone: Negative energy on the ground that deals % dmg of enemy max hp
Cost: 90 / 100 / 110 / 120 / 130 Mana
Percentage Damage: 5 / 6 / 7 / 8 / 9 % (+1% per 80 Ability Power)

Malefic Visions: Sort of poison that if enemy under MV is killed jumps to the next nearest and refund you some mana on lvl 1 need to kill 6 mobs to cast "for free" on lvl 5 need to kill 5 mobs :)
Cost: 60 / 75 / 90 / 105 / 120 Mana
Magic Damage: 80 / 140 / 200 / 260 / 320 (+0.8 per Ability Power)
Mana Restore: 10 / 14 / 18 / 22 / 26

Nether Grasp: One of the best ults in game does great dmg and surpressing enemy that is affected, unfortunetly you can't do anything for 4s or else it will not do it's full dmg (DoT)
Cost: 150 Mana
Cooldown: 120 / 100 / 80 seconds
Magic Damage: 250 / 400 / 550 (+1.5 per Ability Power)

You can have problems attacking with Call of Void at first but you will get it after little practice :)

Malzahar can do serious dmg because of his great bonus from ability power to abilities dmg :) (Call of Void +80% AP, Malefic Visions +80% AP & Nether Grasp +150%(!) AP) Well timed combo which looks like this: Call of Void, Malefic Visions, Null Zone and at last Nether Grasp kills almost every champion in the game :)
Malzahar is great champion trully worth the IP and RP points he costs. For me he is the greatest mage in the game :) and he is good dancer too :P
If you're thinking what champion you should buy and you don't like standing in first line with sword in your hand I recommend Malzahar.