What do I need to research to switch to an internally geared hub? I have a bike that I rather like, but it's geared entirely for high-speed road bike type work.  It's fantastic on the flat areas of the route that I take every day, but I also have a couple of serious hills that I cannot climb with this one (I can climb them with a different bike).

So, I'm looking at the possibility of saving money to replace the entire bike, or to regear it.  An option that I saw today was something like the Shimano Alfine 11-speed hubs.  I've not calculated gear ratios, but it's claimed that they have a very wide range and such a thing would benefit me.

So, if I wanted to retrofit my bike to an internally geared hub, what is involved (and what are the terms I'm looking for)?


size of axle?
distance across the rear fork?
what to do with no-longer-used rear derailleur?
will my existing grip-shifter need to be replaced, and does that entail anything other than just putting the new one on and attaching the wires?
will my entire rear wheel need to be replaced?


I'm pretty vague on what industry terminology would be used in this case.  I'm also trying to evaluate the viability of even doing this as I balance my options for adjusting or replacing the bike to better fit the city I live in.  The only adjustment I haven't mentioned is for me to replace the front chainring (there's only one on this bike) with something a little smaller.  I'd lose level-ground power but gain some climbing power.  And that, really, might be the least expensive and easiest of all of my options.
The first thing you should be looking into is gearing to ensure that an internally geared hub will work for you! The more you pay, the more gear range you get out of a hub, but even the nicest internally geared hubs don't match the spread of standard mountain bike gearing.
If you've decided that an Alfine 11 hub is for you then to answer your questions in order:
-the axle size shouldn't be an issue.
-the hub spacing is 135mm. That's mountain bike spacing typically. Apparently it can be adapted down to 130mm but I'm not going to detail how to do that here
-sell it/keep it/ use it as a paperweight
-The hub will have a dedicated shifter. I seem to remember that there are both trigger and grip shift options. Should fit without issue, though you'll probably have to take your grips/bar tape off.
-Yes, unless you have an incredibly nice rim with the proper drilling that you want to re-use.
You will also need a chain tensioner if your bike does not have horizontal/track-style dropouts, which I doubt it does. I believe there's one that goes along with the Alfine that Shimano sells as an accessory, though I don't think you have to have that particular one.