The boil serves several purposes. It sanitizes the wort, isomerizes (makes them soluble in the wort) the alpha acid from the hops, concentrates the sugars, as well as develops flavours from the cooking process. It’s important to have a good boil, but it doesn’t need to be jumping out of the pot either, just as long as the surface
is rolling over its good.
The wort is typically boiled for about an hour, but can be longer. The longer the boil, the more water is evaporated and the more the wort sugars become concentrated. Strong beers may be boiled longer for this reason. Also, a long boil will start cook the sugars in the wort creating caramel or burnt sugar flavours and darken the colour. The increased boil-off of water also means that there is a reduction in wort volume and therefore beer output. These factors should be kept in mind.
You can add hops at several stages in the boil to achieve different results. Bittering hops are generally added for 60 minutes. After about an hour pretty much all the alpha acids that are coming to the party have been pulled out into the wort (you might get more beyond an hour, but it drops off pretty quick). Hops added for flavour are done so late in the boil, typically in the last 20 minutes or even after the boil is complete. The later the hops are added the more they will contribute to aroma. Hops added with 10-20 minutes remaining generally are for flavouring.
First Wort Hopping (FWH) is when the hops are added before the boil while the wort is just running out from the mash tun. The theory is that the hops will contribute their aroma compounds to the wort (which is hot enough to extract them, but not hot enough to volatilize them) and due to the nature of the wort, this aroma can be “locked in” and survive the boiling process. The science is young behind this, but the results seem to suggest that there is indeed something to it. Sounds like a good place to experiment.
When the boil is finished, it’s important to chill it down below 25 C (75 F) or so as quickly as possible. This is make sure the worst of the critters that might want to take up residency in the wort won’t be so welcome and also, this will ensure that some off flavour precursor compounds that have been boiled off won’t reform.
To chill the wort there are a few options. The simplest one is to put the kettle into a large sink full of cold water, possibly with ice. As the wort cools the water will warm, so it will have to be changed (probably a few times) to make sure it’s working. Stirring the water in one direction while stirring the wort in the opposite direction will greatly reduce the time it will take to chill.
The more common specialized equipment to chill wort are immersion chillers, counter-flow chillers, and plate chillers. There is other equipment that you could use, but these are the most commonly used chillers.
Immersion chillers work by immersing a copper (or stainless, though copper has better thermal properties) coil into the wort (typically 10 minuets before the end of the boil to sanitize the coil) and then to chill the wort, cold water is run through it. The water chills the wort and will actually come out warm (or even hot). Stirring the wort in the opposite direction to the coil will speed this up. This way is faster than a sink full of cold water, but will take 20-30 minuets to chill (depending on the cold water temperature).
Counter-flow chillers work by passing the wort and cold water through the unit in opposite directions. The chiller is made up of an inner copper (or stainless) coil inside a hose (homemade ones use a garden hose). The principle of thermal transfer is the same. The downfall to this is that the wort in the kettle stays hot until the full volume is passed through the chiller, but the wort that comes out it fully chilled quickly.
The plate chiller is much the same as the counter-flow, but instead of a coil, its contained inside a block. There are plates that work doing the thermal transfer.