okay its a common question so heres some info.

induction kits are intended to allowthe engine to draw more air in.
more air means more fuel can be added so more power

there are many types.
i'll try and cover the basics here but theres plenty of different types available.
budget also plays a part here.
the most commonly bought are the straight on the top of the TB K&N,green,pipercross etc type


in that picture you will see a pipercross breather filter as well.these are now an emissions fail(though some have passed MOT's with them)
the problem with this type of induction kit is they sit right on top of the engine so are surrounded by hot air.
not good for performance.
you can fit a cold air feed which helps but is not perfect

now other options involve fitting the filter remotely to move the filter ot a cooler part of the engine
this is liams home made one


if your making your own then you need an 899cc bob for the TB(available from fiat,scrappies etc) a reducing elbow silicone hose either samco or SFS and of course your chosen filter.
obviously there are other options and varients but this just covers the basics

heres arc's with the BMC CDA




this is an induction kit by a forum member named ArturK



again this has proven gains however being a non uk kit it uses an atmospheric crankcase vent(seen to the left of the TB top)
this is now an MOT fail so be aware of this if considering purchasing one of these kits