I use a 40 lt Buffalo boiler from Nisbetts to initially mash in and then boil, once the grain bag has been removed. After the boil I use an immersion cooler in the boiler.
When it has cooled I transfer into a plastic fermenting bucket and add the yeast. After fermentation is complete I keg my beer but bottles, whilst taking longer, take up less space.
As long as you can get your ventilation sorted out during the boil stage (there is a lot of steam and condensation) this set up can easily fit into even the most compact of kitchens.
The actual amount of surface area need for mashing and boiling is the footprint of the boiler, around 18" square.
You will need somewhere warm for the fermenter in order for the yeast to work its magic, temperature at this stage can make a huge difference to the quality of your beer.
My set up is very basic and not at all automated, but if you are looking for more bells and whistles look at systems like the Grainfather and Braumeister.
Check out youtube for a more visual explanation of these systems, there are a lot of different set ups, pick one that appeals most.