I will explain you how doing well with malzahar. I like malzahar a lot because he does well against almost everybody. I have masterie 5 with malza and I love to play with it. He is quit difficult because you have to be posicioned all the time for the fact he don't have any scape. But he kill very easy just pres R and "poof" "YOU HAVE SLAIN AN ENEMY!!!" .
So, let's go!

Pros:
Insane Burst
A lot of poke
Good mana restoration
Easy laning phase
Perfect 1v1

Cons:
No scape
Time damage skills
If they stop your ult you'll do nothing

Malzahar's lane is very offensive. Hit minions and when they are low use your E then basic hit in affecteds. When the AIDS pass throug enemies you'll restore mana. That's the reason why you don't need to buy mana items.
If you're in blue team put a pink in the second brush in the left and the trinket in the right brush.
If you're in red team put a pink in the second brush in the right and the trinket in the left brush.
Warding like this will avoid ganks because malzahar lane isn't safe.

When you want use Q or E in the enemies. Using E will make they retreat a lot of times. When you're in their tower use W to make them retreat more and don't farm. Always try to use 3 hit or skill in enemies to make Thunder Lord masterie cause a lot of damage.
To burst is very simple: If the enemie can jump wait it jump in you then use W+E+Q+R probably he will die.
If they are afraid to go on you, you can go using E+w+Q+R.
Always use Q in enemies before your ultimate. This will give you 100% accuracy.