As a US citizen, she doesn't need a visa to enter Canada. She can come as a tourist. She might be given up to 6 months at the border, although she might have to prove that she has ties to the US etc. Once she is in Canada, she can keep on extending her visitor visa as long as she does it before the visa expires. Or she can go back to the US and come back to Canada - the clock is reset every time she enters. But - depending on her previous travel history etc - she might be asked questions at the border.
She can not work on a visitor visa - so your son would have to support her, or she would have to have enough money on her own for that. In most provinces, she would also not be covered for healthcare.
Once she has lived continuously with him for 12 months, they become "common-law", so he can sponsor her as his CL partner. she can't apply for PR on her own: she would become a PR through family sponsorship.
If he wants to sponsor her before the 12 months, then they would have to get married, then apply - there is no need for the 12 months living together if they are married.
During the PR process (once they have applied), if they apply outland, she won't be able to work. Current processing times for US citizen are about 8 to 9 months (website states 12 but a lot of cases are done a bit faster than that). So potentially, she is looking at not working for about 20 months of not working in Canada...
If they apply outland, she can travel in and out of Canada. If they apply inland, she has to stay in Canada but she could get a work permit after 6 months. For more info on the outland/inland process, read the first thread by Leon - the first page only.
Good luck,
Sweden