[Joppa]

You need to plough through following official documents by UK Border Agency regarding EEA Family Permit, a kind of entry clearance (visa) that you need for your US husband:
EUN02 - EEA Family Permits (detailed requirements for the issue of permit)
http://www.ukvisas.gov.uk/resources/en/docs/1903073/vaf5 (EEA Family Permit application form)
http://www.ukvisas.gov.uk/resources/en/docs/1903073/VAFguidancenotesvisitors (guidance notes)
Family permit is issued free of charge.
There is no general financial requirement, or to show that your husband is financially dependent on you. Just evidence to show that your marriage is genuine and not one of convenience. If you've been married for several years and been cohabiting, it won't be an issue.
Unless there is adverse immigration record (e.g. being turned back at a border) or serious criminal history, EEA Family Permit should be issued promptly (this is an EU requirement).
Then, as Bev suggests, go to the UK consulate website covering your State about practical details of applying for entry clearance.

 

[Joppa]

There is a general rule for you, as an EU migrant, that you will be economically active , earn or have an income at least equal to the minimum levels that trigger social security payments, and that generally you won't become a burden on the state. But you don't have to prove this prior to entry, and as UK has no compulsory residence permit scheme, there is no checks made on you.
I don't think you will have any trouble applying for EEA Family Permit. Just make sure you supply all the documents requested, such as birth certificates, marriage certificate, passports etc.