Hi and welcome to the site!
You're right that you need to find work permits by getting someone here to sponsor you and apply for the permit here. It's a tricky thing to do, but if you want it badly enough, it can be done. Check out the Visa board for more info on how to go about securing the visa.
Finding work here before you have a proper visa that entitles you to work here is tricky. There are lots of job sites I could refer you to, but unfortuantely it is highly unlikely that anyone recruiting will give you the time of day unless you have some very specialised skills.
Also, I believe it is actually 5 years of living here
without being subject to immigration controls before you are able to apply for citizenship. Unfortunately, living here on a work permit won't apply to this time since you will still only be here on a limited visa.
You could transfer over with an American law firm though if you wanted to stay for a few years. That is usually the easiest way to go about getting work here.
Have you been to the UK before? What about it has made you decide this is the right place for you?