Work for Canadian Division

I work for the Canadion division of my IT services company, which is headquartered in Finland, but I report to the US office. I may have to go to the US office for up to 6 months and work out of that office although I will continued to be paid by my Canadian division. I have no intention of staying there permanently, but I will be working and taking training in a software. Will I need to get a some kind of business visa, what do I do about paying taxes?

You will defnitely need a visa of some sort to allow you to work in the US. An L1B intra-company transfer would probably do it.

I may have to go to the US office for up to 6 months and work out of that office

Depends on the term of the employment, if you're only doing it for a few years then the category you want is L-1B, the US branch of the company needs to sponsor you for that by filing an I-129 and you must have "specialized knowledge" to get it, this means bespoke knowledge about the company that someone off the street wouldn't have. You DO NOT need a visa if you're a Canadian citizen, endlessly on here we seem to get people asking about L-1 visas and their idiot employers hiring idiot lawyers to help them get it. You do need some paperwork to go with the approved I-129 (basically some evidence you have specialized knowledge and proof you work for a foreign branch of the same company) but Canadian citizens can apply at a POE for L-1 status, there is no need for a visa, it's a waste of time and money.

The other alternative if this is going to be an on-going situation for many years is "L-1 intermittent", this is basically the same as L-1B except it only allows entry for up to six months a year (total), but it can be renewed indefinitely, L-1B is limited to five years.

although I will continued to be paid by my Canadian division.

You'll be paid by the US division, you have to be for tax reasons, plus they're the ones sponsoring you for the L-1 so you effectively become a paid employee of that division.

The US division will put you on their payroll and issue you a W-2, this requires you to get a social security number, which you get by showing proof of status (your I-94) to the local SSA office.

Each year you will file a 1040NR and a Form 8840 with the IRS and declare any US-source income (mainly your W-2). On the Canadian end you declare the income from your W-2 (converted into Canadian dollars) on your T1 and claim a foreign tax credit. You can claim FICA taxes too because of the tax treaty. You'll probably have to pay some additional Canadian tax on top of it because the rates here are usually higher.

When you fill in W-4 (equivalent of TD-1) in the answer to question 6 you put down "non-resident alien" and they're supposed to withhold at a slightly higher rate.

The best way of approaching this is to file your 1040NR and wait and see if you get a tax refund before claiming a tax credit, otherwise it just makes the calculation more confusing when you do your T1.

You may have to do your research very carefully here. If you were not performing actual work in the U.S., the B1 Status would be a good prospect for you. However from your post, you mentioned 'training and working' which would be a violation of B1 Status. The B1 is not a work authorization per se. It is a business Status that allows certain activities including training where the remuneration paid must necessarily evolve from sources outside of the United States. You meet the criteria since you are being paid by the Canadian division. If you were performing actual work duties in the States, you would require an actual non-immigrant work authorization so the B1 is most likely not a good route.

You'll be paid by the US division, you have to be for tax reasons, plus they're the ones sponsoring you for the L-1 so you effectively become a paid employee of that division.

A few years ago when I had an L1B, I was not paid by our US office, I was still on Canadian office payroll, because I was just going back and forth, my primary base was still Canada. This is what it sounds like the OPs situation would be, so I should think that they would remain a Canadian employee, who also occasionally works at the US office.

If you're directly employed and you earn more than $10,000 you have to be on a US payroll, it's the law. Read IRS publication 597.