Grasp Kog'maw (simple guide). May be applied to other champions.
<RUNES>
Resolve: {Grasp, Demolish, Conditioning, Revitalize} Precision: {Triumph, Alarcrity} 9% AS, 10 AD, 6 armor/ magic resist; depending on the matchup
Can be played: Mid or bot lane. Some top lane matchups (victor, lissandra, Urgot to name a few)
<BUILD> <Highly dependent on the match up, but here are some generalities> First two items usually give resistances 3rd item gives health 4th and 5th item is guinsoos into Botrk
<EXAMPLES>
your matchup is
mid lane
Build:
With the second item, you have some options
If the jungler is mostly ap item, build another magic resist item such as
or
Otherwise, build 
Or if you feel the jungle may be ap but doesn't threaten you and you beat leblanc, build Hourglass anyways
Third item preferably gives HP
Examples:
and 
In bot lane against something like
you will definitely want to rush
into most often
, although if you have a strong laning support go ahead and go
. As Kog'maw you need at least one attack speed item early in order to deal damage, but at the same time it also needs to make you tanky. Trinity synergizes well with grasp, so it is not a lose-lose situation.
<GAMEPLAY> stack grasp with normal autos on minions. Then use w to proc grasp. Unless you are significantly stronger early game do not try to initiate fights. focus on farming and if they get too close use grasp to poke. The actual benefit is that grasp not only makes you tankier, but it also gives you more healing than fleet footwork because of the Revitalize rune. It also makes you tankier over time, giving you over 100 hp typically in the mid game, the equivalent of an extra doran's blade. Grasp also, obviously, does more damage than fleet footwork. However, you do lose the bonus movement speed from fleet footwork, so rushing boots is almost paramount. In the late game you'll have approximately 2.5 - 3k hp, at least 110 of both resistances, 2.00 attack speed, guinsoos, and botrk. This tankiness allows you to theoretically step up more aggressively in teamfights, allowing you to deal more damage.
<BUILD COSTS>Mid game against AP: 6400 gold (not including starting item, potions, wards) 2 tier 3 items and boots
Full build cost: 15800 (note that big ticket items are back loaded, when most other builds front load)
Bot lane against typical ad mid game: 7233 (2 tier 3 items and boots: trinity and wit's end) Trinity on its own is enough to bring you into mid game, but I'm also including a wit's end. You may instead want to go guardian angel or hourglass. In this case, the build costs are 7633 and 7733 respectively)