As a US citizen, you'll deal with the IRS, just as you always have done. You can still use Turbo-tax or one of the online preparation services, if you like. You'll also deal with the UK's tax entity, HMRC, for any income you have when you are living in the UK.
If you are earning income in the UK, there are IRS forms you can use to get credit for taxes paid to HMRC. There are others on this board who are more familiar with the processes - I'm just going through it the first time now.
It's my understanding that if you work in the UK, your taxes will be taken out of your paycheck, so there may be no paperwork for you to actually file with HMRC, if you have no other income but work. If you have foreign income, you will probably need to do a self-assessment with HMRC. They have a website where you can sign up and do most things online now.
Be aware that the UK and the USA tax years are not the same. You'll file your IRS taxes based on Jan-Dec of a year. HMRC runs April - April. On the good side, the IRS allows overseas citizens up to mid-June to file, and extensions are possible. With HMRC there are different dates depending on if you are filing a paper self-assessment or doing it online (if you even need to file one).
If you arrive in the middle of a UK tax year, say, June, you can request "split year" treatment, and anything you will have earned in the US prior to your arrival in that tax year will not be counted on your taxes in the UK.
They tax the individual here, so be prepared for not having deductions for family members (if you have a family) on HMRC taxes. You'll probably be filing with the IRS as married filing separately, to keep your spouse out of the IRS's view. If you arrive and you do not work during the UK tax year, and have no foreign income, you probably will not need to file any sort of tax forms for UK. (I'll let others correct that if it's wrong info.)
You should be fine, once you read through the requirements. If not, there are good people on this board who will help you out, if they can, with explaining how things work. Best of luck with your move!