The hive we started this spring from a nuc* is super active. We only had them a couple of weeks before we had to add a second 10-frame deep on top of the first (this is a Langstroth hive, which is pretty standard).** Last year the packaged bees*** we bought never even filled the first deep before they all left. Today we stuck a queen excluder and a couple of medium honey supers on top of the deeps*; hopefully not too late because they are jammed packed in there and looked like they might swarm: hopefully we did it in time so they'll just make more honey instead. We actually got a second hive* and set it up nearby, dunno if they swarm if they'd just take that over but I guess we'll see, we could always split the hive next spring. This hive is so active it's a little disconcerting having to open it up, even wearing a full suit (we're still both jittery being bee newbs). I dunno how Paul can handle it wearing just a screened hat and gloves. I was sweating my ass off but glad to be fully covered.
nuc (nucleus) is a set of frames (4-6 I think?) that come from an established hive and already have a queen and brood on them. You stick them in an empty deep, stick some empty frames around it, and you're off!
** This is a base with a full sized 'deep' hive body with 8 or 10 'frames' on it, then a board or screen on top of that, followed by a cover. If this is a new hive with no honey or pollen in it you might put a sugar water feeder instead of the top board or screen under the cover, or just put some sugar on the top board. The bottom deep is where most of the brood goes (where the queen lays eggs and they raise new bees). When they start filling that out, you slap another deep on top of the brood deep. This is where they put their honey. You don't harvest from this one-
Once they've started filling up the bottom two deeps you stick a queen excluder on top of those deeps--only lets through workers but not the queen, who's bigger--and then a medium (sorta half-sized) box with emtpy frames on top of it. Or two, or more. The queen excluder is to keep the queen out of the top boxes so she doesn't lay eggs in the frames from which you'll be harvesting honey. The reason you use smaller 'supers' for the harvested honey is that these boxes are HEAVY. Slinging around a full-sized super full of honey is difficult, so you use medium sized or even shallower boxes for these.
Our setup is from Mann Lake and we bought it already pre-assembled and pre-painted from amazon.com. Not the cheapest option but definitely the easiest.
** Splitting means you are taking frames out of an established hive to make new hives. You might do this to increase the number of hives, to keep the bees from swarming and leaving (which they do if they get too crowded or unhappy), or to make nucs. You pull out a few frames with brood, hopefully with some that's young enough, along with the bees on them, a few frames of honey and pollen, and stick it in a new hive body, maybe with a feeder or sugar. The queen and the rest of the bees stay in the old hive. Assuming you had some eggs that were young enough, the other bees in the new hive can convert some of the eggs to queen brood (using royal jelly) and raise a new queen for the new hive. Otherwise, you have to obtain a new queen somewhere and introduce her like you did with packaged bees. You're supposed to do this in the spring so they have time to get established.