Arguably, krogans as a group are the most viable melee kits in the game. Their attacks are fast, high damage and can lock on to enemies from quite far away. All of which is to say that they can be played well without an intimate knowledge of game mechanics and maybe that's why there hasn't been a comprehensive guide up to this point. Up to this point.
Some facts to know about all melee builds, including krogans:
1) The shotgun omniblade is the single most important add-on when you want to kill enemies with your fists. The damage boost is multiplicative, meaning you get 50% more damage after you sum all the other bonuses from powers your strength enhancer and your gear (all of which are only additive). The other weapon mods are also multiplicative but only up to 25%.
2) Most melee attacks will lock on to enemies. The ranges seem to vary but when you get it right, initiating a melee attack when a mook's in your red crosshairs will pull your character into a complete attack. The ultimate example is Batarian hatesurfing. The exceptions are most of the area damage melee attacks and most of the light melee attacks.
3) Smoke, stasis, and freezing will completely screw with your targeting. No big deal if you're a GI or human adept or even a salarian, but your krogan just charged past that phantom is about to get a knife in the back.
4) Melee attacks grant you momentary damage resistance. Usually 50%, but occasionally higher (e.g. Slayer and Batarian scum). You literally become healthier when you melee.
5) Weapons like the Graal, Venom, and acolyte can be discharged while your sprinting to your target or during your melee or to interrupt the inevitable sync kill animations. Use this to keep fighting.
6) Ops packs are a beautiful thing. You've got six. Use them strategically through the match for sustained melee output.
7) All melee attacks bypass enemy shield gate mechanics.
Some specifics about krogans:
1) Your headbutt attack has a small area of effect. You can't trust it, but occasionally you can enjoy it. It's a better alternative to the backhand in smoky situations.
2) You're heavy melee only does 75% damage to armor. If you're talking strictly about damage, two light melees do more armor damage than one heavy melee. There are still reasons to use the heavy too, like greater range and force (i.e. knockback chance).
3) If you equip the batarian gauntlet, you can still do the krogan heavy melee as long us you are sprinting when you push the melee button. Why would you bother equipping the gauntlet? Because your krogan heavy melee will now decapitate.
4) RAGE. Rage is essential to any good krogan punchfest. You get extra DR, extra damage and malicious laughter. Take all three melee ranks in fitness and you only need two kills to Rage (one for the Warlord). Any death by a melee attack counts (as do the Kroguard's Charge kills).
Protip: Any death that happens at the end of your melee attack counts to the Rage tally. If your Claymore GI friend just headshotted your target -- as long as you were meleeing when the head exploded -- it still counts. This more than makes up for the occasional melee kill that fails to tally.
5) Let's come back to the headbutt. It can lock on to mooks. It staggers all humanoid mobs out of actions. It greets, praises and admonishes teammates and enemies alike. It give you some DR during hacks and escorts and pizza runs (though in the case of pizzas, the heavy melee will give you DR and get you there quicker). If there is another krogan on your team, a between-wave headbutt or ten is what must be done.