I have a very good friend from the UK who is wanting to move to the United States and I'd like to sponsor him so he can move here, and let him live with me until he gets settled in...how would I go about doing this?
You can't at least, not in the capacity of a friend and not for any length of time.
You can provide a letter or even an Affidavit of Support to back up a visitor visa request - but since your friend is from the UK he doesn't really need a visitor's visa for a short visa; he can travel under the visa waiver p[program/ESTA for a brief visit.
Anything more than that, are are really only two types of "sponsors" (technically, "Petitioners"): a close family member, and an employer.
If your friend has no close family members here (and even if he does but they are someone other than a spouse, parent or over-21 child US citizen), the only practical solution would be an employer-sponsored case based on your friend's work experience/educational background.
You/your friend need to speak with a lawyer, and supply his resume, to see what might be possible.