Is it possible? I have downloaded a map but can't seem to put it anywhere!

Yep, you can play custom maps with the Steam version of Q3A. After downloading the maps, unzip them and place the pk3 file(s) into:
C:\Program Files\Steam\steamapps\common\quake 3 arena\baseq3

Note: This is for a 'default' install of the Steam version of Q3A. There is more information here:
forums.steampowere.../showthread.php

Thanks Tig!

Yeah what Tig said :).