Usually agencies require a one off payment when they place a nanny with you, around a months salary (the nanny's salary, not yours!) Do check though, some ask for other types of payment and if you go for a few agencies always, always keep all the paperwork from them seperate and mark C.V.'s with the date recieved, if you are sent details of the same girl (or guy) from different agencies and take her on, the agencies may argue over who sent her first and who should recieve the payment, also if you find someone on your own (through wrod of mouth/advertising) and she is with any agencies you are registered with, they may want payment!
The agency should check everything for you, CRB, references, quailifications etc but be warned, some don't bother, you may have to do this yourself.
I am a nanny, have been placed in this position (and others!) and the agency I got the job through didn't call any of my referees, my boss had to do it in the end. I am in contact with all my previous employers (going back 23 years) and I know that none of them were contacted via phone or post.
I do think that if you have time, try to find someone yourself first, either place an advert in local paper, on nannyjob, gumtree, mumsnet!, netmum's, there are others and I am sure others will come along with more ideas. Maybe ask at your children's school/doctor's surgery/toddler group/music or gym group, if you could put up a poster or if anyone knows of a nanny looking for a new position. If all else fails, then go to an agency.
Good luck, I have been doing this job for 23 years and I do not know how a mum chooses the right person to look after their precious children! I mean it must be the most difficult job it is to choose someone.