You buy a house by going up to the plate in front of an empty plot and selecting the buy option there (you will be asked if you want to buy it for FC if you have the rights to do that, so make sure to pick the right one), then buy a building permit from the same plate.

Keep in mind though, most worlds do not have any free plots. That situation won't change until at least 3.3 (or was it 3.4?) when additional housing wards and Ishgard housing area will be released.