It is an Aeonium and I will try to give some general help. Here is a page where you can see lots of pics and read about the genus:
The Aeoniums Database
Aeonium is a genus of leaf succulents from the Canary Islands (mostly) which are winter growers, meaning they grow from fall through spring and rest (somewhat or totally, depending on the plant and the climate) during the summer. They come from a climate with winter rainfall and dry summers, which is why they do so well in coastal California. They like a lot of light during winter, and enjoy some protection from overhead sun during the summer in climates with summer heat. They like regular water through the winter (when the soil is almost dry) but do not like extra water during the summer. Your plant will probably look worse and worse from now through early fall, and you might even think to give up on it, but come September-October it will engage drive and then you will see a rapid turnaround. During the period of decline during the summer, do not give extra water, and provide overhead protection if rain comes at the wrong time or for too long.
The first thing to do is get it out of the water bucket. That will not help and could possibly hurt the plant if it provokes rot in the stem. These are dry growing plants and they do not enjoy wet feet.
I would take a knife and cut the main stem about half an inch below the lowest branch, or some spot in the near vicinity. It might sound like a big sacrifice given you're losing height, but the younger stem will root faster and more abundantly, and the cutting will be more stable in the interim. Make a clean cut straight across (don't break the stem in your hands) then leave the cut surface in a place with good air flow to heal for a week.
Pot up the cutting in a relatively small pot (I'd guess 6" would work) that is wider than deep, with holes at the bottom. Use a soil mix that drains rapidly and is not overly moisture retentive. Only bury the bottom half inch or so of naked stem. Do not water right after potting up the cutting, wait another week and then water deeply for the first time.
From then on out provide strong light, but avoid direct overhead sun until fall. Wait for the soil to go nearly or completely dry at depth (not just at the surface) before watering again. Remember that the plant will not be drinking until it has developed roots, so do not overwater during the coming few months.
These plants do not like extreme heat (especially when it does not cool down at night) and you should avoid watering deeply when it's really hot outside (or oversummer the plant indoors by a sunny window). They also do not like extreme cold (below about 25-30°F, approx. zone 9b). They do best when it is cool and mild, and you will notice dramatic seasonal changes as they go through their cycle.
