Federal and State income tax for US citizen working abroad?

As a US citizen, you'll be allowed to exclude up to about $100k from federal taxable earnings if you meet certain requirements.  See IRS publication 54 for additional information.  Most people have trouble meeting the 330 day requirement.  US states do not follow that federal rule, but unlike federal, states mostly tax income earned in the state.  The exception to that rule is if you're a resident, in which case the state will impose tax on your worldwide income (similar to federal).  So again, you might have issues on the state side during your first year because you might be still considered a resident in your home state, unless you completely and immediately sever all ties to that state (subjective test).

Thank you so much. I have a follow-up question if you don't mind. Do you know if I have to let my employer know that I'll be working in Vietnam?

Can I let my company pay my federal taxes via a W2 and then file a W-2c form, Corrected Wage and Tax Statements form after during tax season? I know this sounds silly, but I am afraid that my company won't let me work abroad. I will still talk to my HR person regarding my concerns, but I fear that they may let me go for wanting to work abroad. Please advise.

I'd asked my company to adjust the withholding on my wages, but that would all that you'd need to them for tax purposes.

You should download form Publication 54 Tax Guide for US Citizens and Resident Aliens Abroad.  https://www.irs.gov/pub/irs-pdf/p54.pdf

Also Form 2555 instructions:  https://www.irs.gov/pub/irs-pdf/i2555.pdf

This is entirely subjective and not based on any qualification other than being a card carrying kibitzer, but I would guess that you do not qualify for the Foreign Income Exclusion (Form 2555) because as you have described it, your planned residence in Vietnam is totally unrelated to your income which is essentially being paid in the state of your employer.  Best to consult a real tax lawyer in the US and be upfront with your employer, although we armchair lawyers will always be willing to give our opinions.   

One thing you could be certain of, for all practical purposes, is that regardless of legality, if you are paid by a US corporation to an account in a US bank there is no way Vietnam is going to be able to tax you.

The main question is : what are you going to do in Vietnam? You cannot just stay there indefinitely on a tourist visa ; 3 months max, renewable in Vietnam once, and then, you have to go out to Cambodia, Laos or Thailand to get a new one. If it is to work, not easy ! You have to find an employer willing to help you with a Vietnamese contract + a work permit + a business visa. You need a layer, who will cost you 500 to 1500$

Good point. According to this site, I can extend my tourist visa up to an additional three months. So I guess I can only stay for a few months unless I apply for a business visa.