An employer looking to fill a position appoints a recruitment agency to produce a list of suitable candidates. The agency then goes through the CVs listed on its books and makes a selection, or actively seeks out possible candidates it believes could be suitable (recruiters are increasingly using online professional networks to find skilled people), and delivers them to the employer for further selection.
Depending on the position being offered, this may involve the agency sending the candidate for interview with the client, supplying the client with a selection of CVs or making the final choice themselves.
When the right candidate is found and hired, the employer pays a fee to the agency. The process costs the candidate nothing. Most jobseekers simply need to apply to an agency to have their details listed and then, in theory at least, the agency should alert them to any suitable openings.