I work for a foreign company, but live in the United States. How do I file this?

It depends on 2 things:

1. If you are a US citizen or resident alien (as opposed to a nonresident alien).
2. Where the work you did was performed (either in the USA or in a foreign location) regardless of where the company you work for is located. Remote work performed in the USA is considered US-source income.

If you are a US citizen or resident alien for all of 2016 and the work is performed in the US, you will report this income (in USD) as US-sourced income. You will file a Form 1040 (or 1040EZ/1040A). You will be able to take a Foreign Tax Credit for any foreign taxes paid on this income. 

You can enter your wages (if no W-2 is going to be sent) under other miscellaneous income:

1. Click on the “Federal Taxes” tab ("Personal" tab in TurboTax Home & Business)
2. Next click on “Wages and Income”
3. Next click on "jump to full list" (or “I’ll choose what I work on” or "see more income")
4. Scroll down the screen until to come to the section “Less Common Income”
5. Choose "show more", then Miscellaneous Income
6. Choose "Other Income not already reported on a Form W-2 or Form 1099 " 
7. Select - "Yes" for "Other Wages Received"
8. After 3 screens, select "Yes" for "Any other earned income".
9. On screen titled " Enter source of other earned income" - select " Other"
10. Input the "foreign wages" and the amount on the next screen

If you are a US citizen or resident alien for all of 2016 and the work is performed in the outside the US, you will report this income (in USD) as foreign-sourced income. You will file a Form 1040 (or 1040EZ/1040A). Since your income is sourced where it is earned (and not by where the company paying you is located), if you met the Bona Fide Residence Test or the Physical Presence Test, you may be able to claim a IRS - Foreign Earned Income Exclusion that would exclude a portion of your foreign source income (up to $101,300 for 2016). You may also be able to take advantage of the foreign housing deduction. TurboTax will guide you on taking the foreign earned income exclusion and foreign housing deduction. Additionally, you would be able to take a Foreign Tax Credit for taxes paid in foreign country on this foreign source income that is also taxed in the US (but only for foreign income not excluded under the foreign earned income exclusion).

TurboTax will guide you on taking the foreign earned income exclusion and foreign housing deduction under Federal Taxes> Wages and Income>I'll choose what I work on (or jump to full list)> Less Common Income (show more)> Foreign Earned Income and Exclusion

If you are a nonresident alien for part of 2016 and the work is performed in the US, you will report this income (in USD) as US-sourced income. Depending on your visa type or if you meet the green card test or the substantial presence test, you will be considered either a nonresident alien or a dual-status alien. TurboTax does not support nonresident alien or dual status filings. However, if you have US-source income, you will be need to file a US income tax return based on your alien status

See this link for more information from the IRS on US Tax Guide for Aliens