Malphite is a dps tank that's pretty easy to play, he's a strong pusher and can easily assasinate almost any t arget if you have the right build. (This one above this text ;) )

Laning Phase

As a solo top, your job is to farm like a boss, zone your opponent and prepare for ganks (whether friendly or enemy). Most importantly, try not to let your tower fall or force your jungler to help you hold the lane. This shouldn't be very difficult between Regrowth Pendant, Granite Shield, Teleport and Malphite's harass skills.

Use Seismic Shard to counter-harass your opponent. When they walk up and smack you or use an ability, hit them back with your Q and Ground Slam if they're close enough. Then play a little passively for 10 seconds and let your Granite Shield refresh. Rinse and repeat, and you should be winning the lane in no time.

Let's say you're laning fine, getting some farm and shaking off harass, but the enemy has too much sustain for you to weaken enough to burst (solo top champions often have a lot of sustain). Now is the time to call for a gank. If your jungler is busy ganking bot or grabbing a camp on the opposite side of the map, don't worry. Just let them know that you're ready for a gank (preferably your ultimate is off CD) and wait for them to get to top lane. Make sure you don't push your lane if you want a gank.

Now, the enemy player may have called for their own gank, and that is why you get WARDS to cover the river. Always keep an eye out to see if your lane opponent places their own wards, so you can let your jungler know to either cancel the gank or get oracle's or a vision ward to counter ward there.

If you're ready for a gank and your jungler is lurking in a nearby push, ping the enemy champion when you're both ready. If your jungler has a good initiation (Warwick post-6), wait for him to exit the bush, then attack. If your jungler has a weak initiation (Trundle without red buff), you may initiate yourself with any combination of Flash, Seismic Shard and Unstoppable Force. Considering the amount of burst and CC Malphite has at his disposal, you should be able to net a few kills before mid game.

Pro-tip: Sudden aggression or a quick visit from your jungler is an easy way to blow your opponent's summoner spells like Flash or Ghost, especially if you've been winning the lane. Post-6 most players are very afraid of the threat of Unstoppable Force, so try to look menacing or have your jungler stop by for a "gank" and they'll be much more vulnerable to future kills. Your jungler can even come back in 30 seconds or so and you can get a clean gank. Just make sure you don't blow your ultimate prematurely if the enemy is just going to Flash out of it.

"Help PsiGuard, I'm in a 1v2 lane and the enemies aren't complete noobs. I can't harass them both enough for a kill!"
Not to worry, Malphite is an exceptionally resilient laner, and can often withstand even the most aggressive harassers without being zoned. Here are some tips to help you "win" a 1v2.

To be honest, all you have to do to win a 1v2 lane is survive it. Keeping up your farm and defending your tower, while not giving up any kills will result in the enemy "losing" the lane. Since they have two champions in lane, they will be sharing both experience and farm. If their combined presence does not result in a kill, a tower destruction or your starvation, they'll be in a very bad position by mid-game, while you'll be outleveling them and your jungler will have free reign of the enemy jungle, as well as easy ganks on mid and bot lanes. Whatever you do, do your best to make sure you don't bother your jungler every two minutes to help you hold your lane. Every minute you hold your lane is a minute your jungler has to farm or gank. If your team is at all competent, you'll have a major advantage when laning phase ends.


Laning Opponents and Aggression

I've added this section due to a good question from Wayne3100.

Q: "I do have a question, however: do you think Malphite is simply capable of holding top lane well because he isn't easily harassed or do you actually believe he is also a strong competitive pick for solo top? Would he only win a lane against squishy melee characters or also tanky champions like Irelia and Renekton (are there any champions he specifically counters and beats 9 times out of 10 in lane)? And finally, is it possible to play agressive with him in lane or would that just fail because Malphite is oom pretty quickly?"
// I think Malphite's resistance to harass contributes greatly to his success in lane. That isn't his only attribute however.

Seismic Shard deals a great deal of damage by about level 3, and it's quite long range and gives you a speed boost while your enemy is slowed. This makes it difficult for enemies to execute aggressive harr*** combos or return your Q with anything close range.

Unstoppable Force is an extremely valuable ultimate when your jungler ganks top. If your jungler has red buff or any CC, it's very easy to pick up a kill. Malphite is also a very strong tower diver, able to tank successive tower hits at early levels, and can tank a tower for a good 15 seconds easily by late game with very little health lost. This makes jungle ganks viable on a tower-hugger.

Is he only good against melee? Well, the short answer is "no," he can keep up with most champions in lane. I've soloed Kog'Maws quite effectively despite their range. Your Quints of Swiftness will allow you to dodge and retreat out of range at a moment's notice, and your Q is a pain in the *** for squishies with no sustain. I would say that my toughest enemy to face would be champions with their own defensive abilities or a high level of sustain, like Mordekaiser or Cho'Gath. If they can withstand successive Qs easily, you will have trouble harassing effectively. That said, don't worry if you can't whittle them down to low health, just farm and soak up XP because Malphite scales really well into late game.

I've been thinking about adding a large section with details about various champions you'll often face in top lane, with some tips on how to avoid their abilities and counter their playstyle. It's quite an ambitious undertaking, so I'm not sure if I'll have the time at the moment. Just wanted you to know I have thought about some of these things.

There's no specific champion that Malphite dominates, but AD and AS based champions who aren't good at taking harass are good targets. I've had success against champions like Kog'Maw, Jax (if played mediocre), Master Yi, Akali, Wukong, etc. Basically champions without good sustain or a defense mechanism are easy pickings if they aren't played incredibly well.

It's possible to be "aggressive" in lane with Malphite, but that basically means a liberal use of Q, E whenever they challenge you and zone them from last-hitting. Generally I play Malphite a little more passively, allowing my opponent to push close to my tower so I can make good use of my passive (it's hard to refresh the shield when you are trying to zone). This position also leaves the enemy vulnerable to a gank, and they are relatively easy to harass when they're that close to your turret. I usually just wear down their health until I get a gank, they b, or I can just ult-slam-Q them to death. It's possible to use more aggressive positioning, but it doesn't suit Malphite as well as other champions like Renekton.

I hope that answers your question.


Team fights

Team fights are fairly simple as Malphite. When the enemy overextends or groups up, initiate with Unstoppable Force, activate Brutal Strikes and use Ground Slam. Target the most vulnerable champion, preferably the ranged DPS and use Seismic Shard to slow them. By this point, the enemy team will probably be panicking and hopefully blown a few important spells on you. While your Sunfire Cape is busy whittling down their health and you're smacking everyone in sight while tanking a lot of damage, your team will rush in, nuke their carry and pick off the enemy team while they're in disarray. In a long team fight, try to protect your carries by blocking CC and skillshots, while disabling the AS of their AD carries (melee and ranged).