Before level 6, your main job is to poke your opponent with Q. You should only do this when your Arcane Comet + Manaflow Band + Scorch are ready (~20 seconds). Once your Q is on its way, immediately run into a bush to stop minions from attacking you. This poking strategy will also allow your passive shield to refresh (~10 seconds).

You should try to last hit minions, but if your opponent is aggressive you will need to wait until you are pushed back under your tower to do this. Only use your W and E if you really need to finish some minions, because it will use up precious mana that could have been used to poke your opponent.

On your first back, buy the item that matches your opponent. If they do physical damage, get Glacial Shroud. If they do magic damage, get Lost Chapter.

Once you reach level 6, keep doing the Q poke until your enemy is about 1/3 health. At that point, you can prepare a full combo. I like to start this by using Q and running back into a bush (like a normal poke), but then surprise them with R->AA->E->AA->W->AA->Ignite->Q combo. Be sure to only initiate if you won't get killed by the tower or minions.

Example of full Malphite combo:
https://u.gg/lol/champions/malphite/combo/1

EARLY GAME:

Sorcery is required for Malphite to be successful in Level 1-5. You will be poking a lot with Q, but you should only do it when Arcane Comet + Manaflow Band + Scorch are ready (~20 seconds). Taste of Blood will also increase your sustain in lane.

LATE GAME:

Ultimate Hunter helps you capitalize on your primary advantage, your incredible ultimate (which can be used to engage or escape). Transcendence will give you extra AP in the late game.

Priorities:

1) Armor
2) Ultimate
3) CDR
4) AP
5) Health

1) Armor: Malphite is one of the few champions who increase damage when they increase their defensive stats. Every point spent on armor will both increase your damage output and your defense against physical damage.

2) Ultimate: Malphite has one of the most unique Ultimate abilities because it provides an ultra-long dash combined with a large knock-up. This can be used for both engaging a new fight or for escaping a lethal situation. (This ult is why we get Ultimate Hunter and prioritize CDR; see next point.)

3) While armor does increase his damage, Malphite's #1 source of damage will be from the base damage on his abilities. Cooldown reduction will enable him to increase this damage, his crowd control, and of course his Ultimate.

4) Malphite's #2 source of damage will come from his ability power. This is due to the high percentage AP scaling on his abilities. Note, he still needs 400+ AP before ability power contributes more than the base damage.

5) Health: Health is a defensive boost for any champion, but for Malphite it will also increase his passive shield (because it is based on max health).

Try not to use your ultimate on tanky enemies. It won't do enough damage and it may end up with you dead. A lot of tanky characters may appear to have low health, but their runes/items/abilities often give them a significant boost while they are low health. In short, if there are multiple enemies, always ultimate the one with the lowest magic resist. You should try to hit multiple enemies with your ult, but only if you are sure you will also hit the target squishy.

Gank a lane whenever your ultimate is ready. Try to gank lanes that are over-extended (pushing towards your tower). Of course, if a squishy enemy is hiding under their own tower with low health, you will be able to survive a few tower hits to finish them off.

In team fights, you should try to bait the enemy team into fighting under your tower, and start your ultimate on an enemy that is within tower range.

NOTE: You will not likely be able to 1v1 the enemy jungler, unless they are low health. If needed, you can often escape with a single Q, but you can also use R, or lastly Flash.