When you fill in the paperwork you'll be asked the minimum rate for which you'd be prepared to work. As long as it's not ridiculously outrageous (e.g. £10,000 p.h.) it's likely that you won't be challenged about it initially.
You'll then be required to prove that you've been actively seeking and applying for jobs. You're strongly encouraged to use the online system provided by JobCentre Plus (which involves setting up a Government Gateway account) and to accept the option to have all of your search and application details forwarded to JobCentre Plus (so they can see what you've been doing). In many cases you've no other choice than to use the online system anyway because the application details for those jobs are only available to view when you're logged in online.
If, say, you state that you're looking for work paying a minimum of £12 per hour AND you can prove that you've been finding lots of jobs advertised at that rate or higher (and, of course, that you've been applying for all of them) then you probably won't find that your minimum pay requirement is challenged (at least in the short term).
However if you keep saying that you've not applied for many jobs because you couldn't find anything suitable, you'll be expected to widen the fields for which you're applying AND to reduce the amount that you say you'll work for. Then, if you're still not applying for several jobs each week, you'll be specifically asked if you'll work for the minimum wage, with the obvious risk of losing your JSA if you say no.