I don't main malz (or really even play him), but here's my general take on him (from playing against him or watching streams):
Your e (space aids) is amazing for safely clearing waves. Try to make it bounce throughout the whole wave once you get a few ranks in it - do this by doing enough damage to each melee minion that it passes on to (and it alone should be enough to kill casters). You may need to auto the melees before using e, or use your Q on the melees.
You get mana back for last hitting creeps. Make sure you get the last hit when possible, don't rely on your e or w, add in that auto attack towards the end.
Your Q is an AOE silence. This can WRECK teamfights, or even just your lane opponent in ganks. Silence prevents summoner spells too. If you're receiving a gank and your jungler cc's your lane opponent, use your Q while they're cc'd so they can't flash away right after.
Be careful with how you use your R. Recommend you play a lot of normals first to get used to it. R seems good, but can be wasted far too easily. If the damage to get the kill isn't there (e.g. it's a 1v1) it's probably not worth using R unless you need the cc to save yourself (get cooldowns back). If you think you're engaging 2v1 and you use R, but other enemies show up, you're a sitting duck and an easy target for them. Basically, when you use R, you cc yourself too, in reasonably close range. It's really easy to use R from a not-great position, and since you're squishy you die instead.
You either want to use R for picks when you have allies around to protect you, or in teamfights when you have a good tank in front of you.