I have family in the United States. How long would it take for me to apply for a work visa and go out there for say 6 months?

it's not about to happen

Employers who sponsor people for work visas want an indefinite commitment. Not 6 months. It costs many thousands of dollars to sponsor a work visa, so they will not do it if it is not worth their money.

You cannot apply for any employment visa. Only qualified employers who first prove there are no Americans qualified & available for the position can apply for employment visa for their qualified foreign employee. If you only have a bachelor's degree, forget it. Half of US bachelor's degree grads cannot find work in US. You'll need minimum of master's degree + experience in a STEM occupation to have any chance of competing for a job with employment visa.

There are some short-term employment visas for seasonal work, such as ski instructors, waiters, etc, at hotel/resorts. But beware of the many scams for these! Also pay is far too low to cover the costs of short-term housing in resort areas, even if you share with a bunch of coworkers. So unless the resort has some sort of dorm accommodations for temporary employees, you will lose money! Of course, if you are world-class skier (Olympic or world champion) & can instruct, you might get decent pay at ski resort for a few months.

Unless you have an immediate relative (parent, sibling, adult child over 21) who is a US citizen & who qualifies to sponsor you for immigration, if they are willing to sponsor your immigration, it currently takes up to 13 years to get immigration visa, if approved.

In order to get a work visa you need to be sponsored by an employer who certifies that he can't find a US citizen to fill the job.

Not enough information to know whether you can get a work permit. The fact that you have family in the US is irrelevant and may be a negative unless this is your spouse. Why you mention Canada is a big mystery.

The easiest work visa to get is the L-1 intra company transfer but to get that you need to be working for a company in the UK that is willing and able to transfer you. Most will not do that unless you commit to a longer stay than 6 months.

The next easiest is a J-1 training visa. These used to be given out like lollipops but they have tightened them up. Now you need a qualified sponsoring employer not just a friendly accountant doing you a favour. Some larger companies do this with seasonal employment but those are pretty low end jobs.

You might want to look at a student visa if you are willing to spend money. Master's degrees are unfortunately two years in the US but those at the top end can be excellent. There are also shorter courses that you can consider such as a 12 week programming course.

The application takes little time. Mitts the approval that takes time.

Too many variables to answer. Family in Canada is irelevant. IN case you didn't know, that's an entirely different country.

So, what is your degree? Is it in a field in which we have need? Do you have a job? As a European, you can't just come and then find a job...do you think you're Mexican?

Finally, if you just want to come to the US as a tourist and not work, that's simple to do. A tourist visa for six months is easy.

just cross the mexican border and stay as long as you want like all the rest of the immigrants do