Check they are a member of a scheme provider, ask them and ask for registration number, then contact them.
These are the scheme providers:
BSI
British Standards Institution
01442 278577
ELECSA
EC Certification Ltd
0845 634 9043
NAPIT
Napit Registration Ltd.
0845 543 0330 - Fax: 0845 543 0332
NICEIC
NICEIC Group Ltd
0870 013 0382
Method and way of payment should be agreed between you.
I like to have 20%-25% up front for materials, then I am quite happy to arrange instalments depending on the size of the job, but leave a little over for completion of work and certificates.
The certificates will vary from provider, but there will be similarities.
If the electrician is designing, installing and inspecting and testing it should be a one signature cert.
You should have at least four pages.
Link to some forms, click BS7671:2008 Right hand side of page this will download you copies of forms.
It's the 'ELECTRICAL INSTALLATION CERTIFICATES NOTES FOR FORMS 1 AND 2' (starts at page 5) this Certificate is only valid if accompanied by the Schedule of Inspections and the Schedule(s) of Test Results.
http://electrical.theiet.org/wiring-regulations/forms/index.cfm
But now you will know how easy it is download and print certs and schedules, so just because they give you a cert, does not mean they are legal. So don't take that as cast in stone
If the electrician is not a member of a scheme provider, this does not mean they are operating illegal either, but they must be a building controls notification in place prior to work starting.
This can either be applied for by you or the electrician, they often come with quite a tasty fee attached.
You can contact your local building controls officer and they will tell you if an application is in place.
But again the electrician will need to produce certificates as linked to, for building controls and yourself.