There is no "size" unless you know what chunks will spawn Slimes.
I can't point you to any online tools since half of them don't work, so just keep digging a 3-high room with torches being 5 blocks apart until you find them....
After you locate a slime chunk (16x16 meters), dig out a room that is at least 3 meters high and that is on or below Y=40. Read the wiki for more information, including how to locate slime chunks (http://minecraft.gamepedia.com/Slime).
If you're down digging tunnels below y=40 and you happen to run across a slime, then yes you can just open up a room. No need to go more than 3 high.
If you look at one of the slime finders and find a chunk, you can narrow down your room more.....but you also need to light up caves around that area all the way up to surface I think.