I have to say I always find these questions mildly amusing because TN-1 was expressly designed for your type of situation, but people seem to think it was intended to allow you to stay in the US for ages with endless renewals!
Yeah, if you fit in the NAFTA category, they give you a job offer letter, you compile all your qualifications etc., you get TN-1. You go and visit as and when under the terms of whatever job it is and do the work. Basically the job offer letter says you will enter for say, periods of a week or two over a total period of a year to do whatever job it is and then followed by the job description, what you're going to do and why that fits into the NAFTA category, etc.
Yes, it does affect your taxes, how exactly is hard to say because you're probably going to be in the "proportional payment of tax" situation in the new tax treaty, so there are no specific instructions as yet.
The Canadian end is fairly straightforward, the only difference is that you claim a foreign tax credit for any income tax (not social security) paid in the US, the general guide for the T1 explains how to do it.
On the US end you file a 1040NR and an 8840, helps a lot if you're directly employed by the US company, because then you just get a W-2 from them for the work performed in the US and that makes filling the tax forms in very easy indeed. (Note, you MUST state on your W-4 when you start work with them that you are a non-resident alien). And according to the job offer letter you are employed by them so that's it.
If you want to be self-employed in the US, ugh, put on your glasses and pull up your chair because you're going to have to do a lot of reading. Technically you can't do it in TN-1 so I won't bother boring you further.
The only slightly tricky bit with your US employer is that NRA withholding is done differently than for resident employees, tell them to read pages 22-26 of IRS publication 515.
Also have a read of this:
http://www.cra-arc.gc.ca/E/pub/tg/p151/README.html
It doesn't really help much but it gives you a general overview.
Don't get too worked up about the "significant presence" test, you live in Canada, that's where you're resident, the end.
Steve.