It really depends on what company you work for and how long.
If you are American and work for an American company AND you are physically in Canada for fewer than 183 days in a year, your taxes are all US because the US and Canada have a tax treaty. Your employer decides where to report your wages for unemployment - you can work that out with them. You will not need to file a Canadian tax return.
If you are physically present in Canada for 183 or more days in the year, you have to file a Canadian tax return. If your employer has not withheld any Canadian taxes for you, this could hurt. So, you have to know in advance whether you might be there for that long and start withholding at the beginning if you will need it. If you are American, you still also need to file a US tax return but you can claim a credit on your US taxes which basically exempts the first 80k (or less if you made less) that you earn in Canada.
If you work for a Canadian Company, they will handle your taxes and unemployment like they would for a Canadian starting on day one. If you are American, you still have to pay taxes on this income to the US. But, you can claim an exemption against your US income taxes for the first $80k that you earn there. You have to file a US tax return no matter what. You will also pay into Canadian Social Insurance and may be entitled to a benefit when you retire if you earn enough for long enough.
You need a work permit. The employer who hires you has to provide you with a letter from Human Resources Canada that says that you won't be negatively impacting the Canadian Labour Market. It is called a Positive Labour Market Opinion. You need to give this to the Immigration officer at the border, along with $CDN150 to get your Employment Authorization (work permit). An EA can be good for up to two years, but only if you work in the same profession. They decide how long it will last, but you can ask them to make it for as long as possible. You will not likely get one that is good for longer than a year. Sometimes, they get stingy and only make it good for a month if you tell them that the job is only a month long. Ask for a year.
If they ask you if you want to import your car, say NO. You don't want that b.s. with the import duty, licensing, and insurance. Just make sure that your insurance will cover you in Canada and get an insurance card from your agent that is good in Canada. It's a special card, your regular one won't do.
Then, you can take your work permit to HRC and get a SIN. This is a temporary Social Insurance Number. You might need it.
If you are working in Ontario, (not sure about the other provinces) you can go to get a Provincial Health Card, which entitles you to free government health care as long as you are a resident of Canada. (Having the work permit makes you a temporary resident of Canada)
If you are getting paid in $CDN, you will want to open an account in a Canadian bank. This is not like opening a checking account in the US. They don't run the banks the same way as here. What you probably want is a "current" account. You can also get a savings account that you can write checks against. You can also get a US Dollar Account, but you probably won't need it unless you need to send money home often. This is something that almost all Canadians have because they travel and do business so much in the US. It is a savings account, but you can write checks on it if you want to.
They still use passbooks for bank accounts - like the one your grandma used to have. You can even stick it into the ABM to get it updated. But you can usually just ask them to give you a monthly statement instead.
Anyway, you need an appointment to open an account at most branches. If your employer writes you a paycheck at one branch of ScotiaBank (for example) you may not be able to cash it at a different branch of that bank. That is why you want an account - so you can deposit the check instead of driving to the branch that will cash your check. Then, you can ask them to convert your money into US when you come home.
Your account will be specific to the branch where you opened it. You can still do business at other branches, but any management of your account - like changing an address - has to be done at your branch. So, get their business card. The ideal situation would be to get the employer to pay you in US dollars so you can avoid having an account there. You ought to ask for that up front.
While living in Canada, remember that merchants don't accept your debit card unless it is an Interac card from a Canadian bank. BUT, your Visa Check Card or MasterMoneyCard work like a credit card too - without the transaction fee. You also get the best exchange rate this way. If you MUST exchange cash, do it ONLY at a BANK!!! You will surely get ripped off anywhere else. Your American ATM card WILL work in the ATM's in Canada (they call them ABM's).
This isn't something you want to do just because you can. It is difficult, frustrating, and expensive to work in Canada. If they make it worth your while, take the job. But the money isn't likely to be that good. So, the only reasons to work there are if they pay a LOT, if you can't get enough work elsewhere, or if you want to live there. (but you can never immigrate to Canada on a Work Permit. You have to leave and come back on an immigrant visa) Like Jim, many Americans who work in Canada do it because they have married Canadians. This is a life choice - not an alternative to working at Limerick. But, you may get some work that is during the "off-season" in the US. If that is the case, I recommend trying it at least once if you can. Just don't be disappointed if you decide to work at Darlington instead of a US plant and find that there is a lot less money in your pocket because of it. They don't work as much OT as we do - even during outages - and they don't have to pay OT until after 44 hours in a week. But, their outages are much longer. The people are terrific to work with. It is a VERY different environment. Drug testing is unconstitutional. You will wear a lot of plastic and suck a lot of rubber. You'll take a lot of showers at work. You will learn how stupid and unnecessary the $1 bill has become.