Would they need a special work visa, and if so how difficult are they to obtain?
To just come over here to work is difficult. If you are sponsored or funding yourself; or if you have graduate skills that a UK employer wants, that can be done. To just turn up and start looking for work makes you an illegal immigrant.
If you can raise the funds, you could enrol as a student and then you would be able to get casual work in a bar or McDs etc. This is not strictly legal but accepted. The problem arises if the course you enrol on does not care too much if you actually turn up. This has been a problem in the past, especially with Asian ‘students’ and is supposed to have been stopped.
Here is the official website: Visas and immigration - GOV.UK
It would depend on what you’re trying to do. Are you going there as a student? Are you going with a cultural exchange organization? Or are you thinking of backpacking and picking up day jobs?
It is entirely legal to work as a student in the UK (up to 20 hours a week during term time and full-time during the holidays): http://www.lse.ac.uk/intranet/students/ISIS/currentStudents/WorkingduringStudies.aspx
What isn’t legal is to register as a student and then not actually attend your course of study in order to work.
Of my American friends who are in the UK, all of them have either come over as students or are sponsored by work permits. I don’t believe US citizens can just turn up and legally work here, even part time, but I’m not entirely certain of that. Generally, for non-EU citizens, the process involves having a firm job offer as well as sponsorship, which isn’t exactly cheap but also isn’t too onerous, as I understand.