If someone stays at home because they can't find the type of job they want, are they included in unemployment numbers? Say someone is looking for a job, but the ones they can find either don't give them the right compensation (businesses pay them too low) or is not the type of work they're looking for. So they stay at home until they find one. 

Is such a person considered to be unemployed by official data? I understand different countries may have different policies about this -- but how is this predominantly tackled?
This may vary depending on the country. But for the US, there are 3 criteria:

People are classified as unemployed if

they do not have a job;

have actively looked for work in the prior 4 weeks; and

are currently available for work.



Criteria #1 and #3 are fairly straightforward. Criterion #2 may be a little subjective and so we have the following clarification:

Actively looking for work may consist of any of the following activities:
Contacting:
    An employer directly or having a job interview
    A public or private employment agency
    Friends or relatives
    A school or university employment center
Submitting resumes or filling out applications
Placing or answering job advertisements
Checking union or professional registers
Some other means of active job search


So if your someone has actively looked for work in the prior 4 weeks (which includes the above activies), then she is counted as unemployed. Otherwise, she isn't.
Source: BLS, &quot;Who is counted as unemployed?&quot;, which also gives some of the major questions (in the BLS survey) that determine employment status.