Help with becoming resident in the US from CANADA...

so how do they show this proof, would it be at the airport or do they need to do it before hand?

It needs to be presented at the POE and it needs to be as plentiful as possible, the more the better. Bank statements, T4s (equivalent of W-2), rental agreements, property titles, copies of tax returns, etc.

The more she has the more likely she is to get in. The law requires proof of an abode outside of the US.

I had this exact experience, you do not need to tell them at the border anything that they do not ask you. You are allowed 6 months as a visitor so book your self a open ended rnd trip ticket, tell them you are going to visit a friend, maybe for 2 weeks or 3 weeks, dont act all shady, (the guards see thousands of people every day DO THIS) and come back with in 6 months. If you stay longer than 6 months than you had best figure out what your long term goals are before you go back home, because re entry later will not happen.

I wouldn't recommend that because in the entry record it will say "2 weeks" and if it turns out you stayed significantly longer then it will make them more suspicious the next time. They keep those records for 75 years, so it means you have to remember to keep your story straight for the rest of your life. To them it's just one page back in your entry record, to you it could be years and years, you won't remember when they start questioning you. "Oh yeah once I stayed in the US for six months, that was like 15 years ago though." "Oh really, here it says you were only going to stay for 2 weeks, so what is your intention today?"

Obviously intentions may change during a visit and you stay longer than you intended, but then you only have to remember it truthfully if that happens. I had a CBP guy question me once about something in my entry record from nearly 20 years ago, it does happen.

If they think you're misrepresenting your intentions, then you're in trouble.