Elise,
You actually have to get your Federal Employer ID number first. Which you can do online through the IRS website (scroll down to the apply online now link):
http://www.irs.gov/businesses/small/article/0,,id=102767,00.htmlI think it give you the number right away, so you can apply for the NE tax ID number, but that you will have to submit and then they send it in the mail. But it is pretty fast, mayb a week.
Then you can file form 20, the NE Tax Application to get your tax id number:
http://www.revenue.ne.gov/tax/current/fill-in/f_20.pdfAll of this is free, don't pay for it. There are websites that make it seem like you have to pay, but they are scams.
Best of luck,
Liz