What do I need to attach to a camera to make umbrella lights go off? Are all umbrellas the same? Home studio?

A few things. At most, this will be good for portraits. No 3/4 or full length shots. You should find out what power these units are - mentioned in watt-seconds or Guide Number. Very surprised that in all the description that this was not mentioned. How to trigger it? If you don't have a PC socket, you can still use a PC cord to trigger one light - the other uses an optical slave, and when it sees the first strobe flash it will go off. You would need to purchase an adapter that fits in your hot shoe and has a PC socket in it. Around $10 on eBay. You can also buy a wireless outfit. If you buy one trigger and one receiver at a place like www.gadgetinfinity.com, I think you'll spend about $40 (not much compared to pocket wizards, which might be $500, but a lot compared to the kit you are considering). It is up to you as to whether you will get your monies worth out of this. I just used this example to someone looking at inexpensive starter kits: The local community college charges about $300 for a photography course. If you buy this equipment with the intent of learning about lighting, and you actually put it to use and learn alot, well then just like a college course, it will be money well spent.

Another resource you should check out is David Hobby's "Strobist" blog. Pay particular attention to "Lighting 101." (link below)