US citizens can't apply for the ancestry visa. You need to be a citizen of a Commonwealth country (eg Canada).
If your grandparent was born in Northern Ireland (or Ireland) you could apply for Irish citizenship - with an Irish passport you could live freely in the UK and become a British citizen after 5 years residence.
If you can discover in your background eligibility for the passport of most other European countries, you can also live in the UK.
Otherwise, unless you can find a UK employer to sponsor you for a work permit , or unless you're wealthy enough to be a business or investor migrant to the UK, the realistic option remaining is the Highly Skilled Migrant Program.
It's not that easy for US citizens to live in the UK. A lot of Brits would like to live in the US but can't, for pretty much the same reasons.
A more roundabout route to the UK might be migration to a Commonwealth nation like Canada. If you migrated to Canada (assuming you'd have a chance to qualify), you could become a Canadian citizen after three years (under current law) and then potentially apply for the UK Ancestry Visa as a Canadian citizen. Of course there's always the risk that because of a change to the law somewhere or your personal circumstances, the plan never works out - you'd have to accept that risk. You'd also have all the costs of establishing yourself in Canada, including tax issues.
Originally posted by plumpudding
I would like to obtain information on how to successfully obtain the right to work and stay in the U.K. I am a 40 year old u.s citizen with a Bachelor's degree, working full time. I'd like to go to the u.k to experience living & working for longer than 6 months! Can anyone tell me how I can remain in the uk and look for work at the same time? I do have family in Uk, and also a grandparent that was born there. However, and tell me if I'm wrong, but I don't think U.S citizens can apply for the ancestry visa. Is that correct? It seems that immigrating from the u.s might be a difficult task. So, what would be the most practical and sucessfull way to go about it? It seems so complicated!
Any replies are appreciated! Thank You.