I can certainly understand "queasy". This is typical, except for those, who as guya says, do "
not know yet that s/he is required to file."
One of the professional tax preparers who contributes to the Facebook group "US Expat Tax Questions" writes, "
I always recommend my clients to try to do it themselves first." He recommends TaxAct. If you are pretty good with reading, numbers, installing and running computer software, and your sources of income are fairly simple, this might be the way to go.
TaxAct has some versions that you can use online in a Q&A format. But I think it is easier to work directly with the forms. To do that you can buy the $29.95 "Plus" download version of TaxAct to install on a PC. You will find it has all the forms you need, ready to fill in (1040, B, 1116, 2555, 8965, possibly 8938), and other forms mentioned by forum members above. The TaxAct program includes all the form instructions.
Start by finding records of all your sources of income for the calendar year, say 2015, and converting them to dollars. This may mean going back through your month payslips and bank statements. You can use the IRS year average exchange rate found here
https://www.irs.gov/Individuals/International-Taxpayers/Yearly-Average-Currency-Exchange-Rates.
Now fire up TaxAct and fill in your general information (name, address, etc). Next create a W2 for your wages, say £30,000 (before deduction of any tax or national insurance). TaxAct will insert the right numbers on line 7 of your 1040. You can then exclude this earned income from US tax using 2555, or or take a tax credit for your UK tax paid using a 1116 general (1116 Worksheet - manual entry). If you also have, say, £100 gross bank interest in 2015 and you are taxed at 20% in the UK, you put this in a worksheet called 1099-INT. It will then automatically show up correctly in Part I of schedule B and line 8a of the 1040. You can then take a tax credit for the £20 UK tax which you have paid by selecting a Form 1116 worksheet for 1099-INT, and this will create the appropriate Form 1116 passive, and put a tax credit on line 48 of the 1040. Alternatively, you can just ignore this Form 1116 if you think taking a small tax credit is not be worth the candle. You would do similarly for interest from a cash ISA, except that you will not be able to take a tax credit.
The first time around there will be overhead in reading and learning how to complete these forms, and deciding which ones you need. If your sister's circumstances are similar to yours, maybe she would let you see her returns, and you can learn a lot from that as an example. Dividends, buy-to-let income, income from UK investment funds, capital gains, ... will require additional forms. One possible strategy is to hire an well-qualified accountant to do it for you. At the end of the first year you can decide whether you could do it yourself in subsequent years.
It helps to keep very good records throughout the year. Keep a spreadsheet, and update it each time you receive any income (end of month pay, bank interest, etc), making a record of any UK withholding tax that has been deducted.
You asked about finding forms for years other than 2015 so you can prepare for 3 years of tax returns for streamlined. Try googling "1040 2012", for example. You will find it. Also TaxAct lets you buy previous years' programs, which will then compute the right tax, exemption amount, etc, for that year. If I were you, I would start by doing the 2015 return (not for streamlined), and once you have learned how to do that, then go back and do the 2012,13,14 (for streamlined).
Long term, you will want to decide whether or not you want to keep US citizenship and continue making US tax returns for the rest of your life. Some people have written that
coming into compliance is not really the problem - it is
remaining in compliance that is the problem. This includes the annual hassle of filing US taxes, and accepting the fact that you cannot benefit from those things from which ordinary sole-UK taxpayers benefit - such as the annual tax free £1000 interest, £5000 dividends and £11000 capital gains allowances, inability to invest in UK funds, filing returns about gifts to a non-US spouse, etc. ...