Will I need to pay both countries?

Hello, I'm at work so I didn't have time to search for an answer for this question, but I've been working and living in the UK for 1 month and I see on my paycheck that UK taxes have been taken out. I'm going to be a bit rude here and announce my salary for the sole purpose of finding out the correct answer to my question. I'm single, under 65 and earning £20,000 per annum. I understand that I need to file taxes for the US. Am I paying taxes to the US then? I'm sorry but I don't understand much about this thing since I'm newly out of college and they don't teach this kind of information there (which they should). So once again, am I paying both countries? Am I getting that money back? Do I need to start saving money from each paycheck to pay the US in April? How much do I need to give them roughly?

THANK YOU!

Quick answer:  No, you'll only pay tax in the UK.  You shouldn't owe any US tax on your UK wages.  You must still file an annual US tax return, but you will owe no tax.

Long answer:  There are always exceptions!  And as your income grows, so will the number of exceptions to the rule.  I would highly recommend seeing if your employer will pay to have your tax returns (both US and UK) prepared for you.  This is a benefit at many companies.  Failing that, hire someone to assist you on your UK taxes, and use a tax programme like Turbotax or a cheap stateside accountant like www.taxlogic.com to do your US returns.  When your income gets to the point where you're ready to invest, plan on spending some big bucks first to pay for a UK-based dual US/UK tax specialist.  This way, all those exceptions will be accounted for and you won't be stung by a major hidden tax trauma that isn't readily apparent to the layman.