Traditionally I go for the first build and the second build is more for fun matches, the third one is experimental. Heres brief explanations of each though:

First Build:

The first build is a pretty standard tank build focusing on armor since his ground slam scales off of it. So your damage potential is lower but your durability is increased with armor and MR.

Second Build

The second build is a little more offensive and focuses highly on Malphites passive which gives him shielding based on his health. His skills will deal more damage because of his increased AP while still having relatively high durability and a more effective passive.

Third Build

not very flushed out at all more of an experiment with AD malphite as such I won't be explaining it in the guide at least for the time being.

For runes I go with MrP Marks and armor Seals on both builds because the MrP helps with your harass some on your shard and obviously Armor is super useful for malphite.
On the first build I go for MR glyphs because its nice to have some MR when you're a tank and Armor Quints once again malphite, armor, useful.
On the second build I go for AP quints and glyphs to charge up your AP a little extra.

For the first build I go 0-21-9 to get Defense as a tank and in Utility mainly so I can get the clarity mastery which makes you very helpful as a team player during team fights or when your lane mate is low on mana and you are too just use clarity gets you and your whole team back in action for the team fight so theres no OOM's
Second build I go more offensive with 9-21-0 still want to be tanky but get extra points for AP CDR and MrP

I always go Flash and Clarity with malphite because Malphite is very mana dependent (Note: getting Blue buff = good idea). Flash is awesome as offensive and defensive skill for Malphite. It works very well in conjunction with his ult so you can dash in deal some damage then get out if things dont go well you can also use it in place of your ult as in flash in Ground Slam Seismic Shard. Consult skill section further for skill combinations etc.
Teleport and Exhaust are also decent choices if you want to push more or be more offensively oriented.

For Skills I always focus on maxing Seismic Shard first because its such a useful harass tool while your laning. On the first build I prioritize Ground Slam second because it scales off armor and becomes your most useful skill for farming and teamfights. In the second build I go for Brutal Strikes extra sooner to make up for the lack in armor inherent in the item build.
This skill is used primarily as a harass skill in the laning phase try to get off a shard on the squishiest hero in your lane it's also a slow so it works good for chasing and escaping just throw a shard out whenever you can. In the beginning you have to be careful about mana but thats why we have clarity and you should get the blue buff once you get around lvl 6. This is your main Damage skill in the second build since it scales off of AP

The passive on this skill helps with farming and the active is useful in giving you some extra durability and some extra attacking power so if your running away about to die don't hesitate to use it. It will help. It will also boost the damage on your Ground Slam so a W,E combination is very useful.

This is your main farming skill and damage skill for the first build since it scales off of armor and as I said under Brutal Strikes W,E is always a good combination. See Farming for further details on using this for farming.

Your Ult is a good initiator as it has knock-up and it has good range. Basically use it for teamfights when a bunch of heroes are bunched together (try to hit at least with it) this can also be useful for getting a kill in your lane as well. (And although not really a good idea you can use it to escape which is somewhat of a waste but if your going to die if you don't use then not a terrible choice)

Combinations

Your most basic combination as I mentioned is W,E ( ) It gives you a boost on the skill damage and your AD so it's good for attacking.

Other wise you go R/ ,W,E,(Q) ( / ). You initiate with the stun boost yourself then use ground slam to hit everyone you just knocked up and hunt down the survivors with Q.

Core Build

-> -> -> ->

I like to start out with boots for the extra mobility and then I go into Boots of Swiftness because it gives you the right amount of speed for harassing. You should be able to throw a Seismic Shard at an enemy by a tower and run away in time assuming hes not too far behind the tower. Then I get a Sunfire Cape because it makes farming a piece of cake. After that I get Warden's Mail because it has some good stats that you need some hp-regen and builds into Randuin's Omen. This part of the item build is the same for both builds so no matter which one you set up masteries and runes for you can always switch to the other at this point and you won't lose much.

First Build Items

-> ->
I go for FoN to round out your tankiness a little bit although, Banshee's Veil and maybe even Warmog's Armor would be good alternatives, and picking any of those three are fine good choices. Randuin's omen is an absolute necessity you already have the Warden's Mail to build into it. It has great stats and a super useful active you cannot go without this item. Next I go for Frozen Heart because it gives you a lot of armor and helps with using your abilities (mana and CDR).

Last Item:
/ /
For choosing my last item I usually pick between these three depending on the situation. If I haven't died at all and I haven't really had to tank or I'm tanking very effectively I would go for Zhonya's Hourglass it give you a decent amount of armor boosting your Ground Slam more and gives you a nice amount of AP so that you can deal more damage with your other skills ( ). Otherwise If you've had to tank a lot and the game is really close make a choice between the other two if they have a really strong AD carry then go right for Thornmail gives you a bunch more armor and an awesome passive. If you're dying a lot or the other team has more casters go for Guardian Angel it revives you if you do die and gives you some armor and MR which will help you out.

Second Build Items

-> -> ->
So for this build we go for health to boost your passive and AP for your skills. I go to RoA first because it's a growing item and we should give it time to grow. After that I go for Zhonya's hourglass because it gives armor as well as a good amount of AP. Then I go for Rylai's for another health boost and adding onto your AP. I finish up by going to Randuin's Omen because for me this is the quintessential tank item so it fills out your tankiness very nicely.
Other Notes:
If you find you're not tanky enough as you go through the match you can always build to randuin's omen earlier and I often end up doing this. On the other hand if your team doesn't need a tank and you want to deal more damage you can sell your Warden's Mail and go for a Rabadon's Deathcap, Nashor's Tooth or Lich Bane. I often go for the Nashor's tooth for the bonus attack speed and the extra CDR which is very useful

For farming basically what you want to do is attack all minions a little bit as you damage with your Sunfire Aegis then last hit them with Ground Slam. Brutal Strikes is also helpful here since your normal attacks will have some AoE damage.
Otherwise just try and keep your shield up at all times. If your getting harassed just walk back and regen your shield then come back up to farm and return their harass with Seismic Shard. Occasionally I like to waste my ult and take someone down because I have the power but generally it should be used to hit multiple heroes.

Just a quick summary of what you should do at what time.

Early Game

Harass with Seismic Shard, try to keep your shield up it increases your survivability

Mid Game

Farm with Sunfire Aegis, Ground Slam and your Brutal Strikes passive. Look to help out teammates in teamfights and tank damage for people if necessary.

Late Game

Protect your carry best you can tanking damage and initiating teamfights with Unstoppable Force and work on pushing lanes with your Ground Slam (for Build 1) or help gank enemies (for Build 2), your slow is useful( )