I'd say it is quite easy IF you use the CD-ROM and Internet site which HMRC provide to employers. The Employers CD-ROM has improved a great deal over the past year and you should find answers to most queries you have on their website, or you can call the New Employers helpline who will assist you.
Starting point if you have never been an employer before, is to get the New Employers pack from HMRC.
First Steps to becoming an Employer
Probably best for you to call 0845 60 70 143 and register via phone - though you can do it on-line, but if you phone they will talk you through anything you are not sure about.
For the first pay run, I've written out an example. For the example I used the manual method, but you will find that using the Employers CD-ROM makes it a lot easier. Paying Nanny For First Time Example
Details regarding when you actually pay the nannies tax/ni on your nannies behalf, and your Employers ni, will be sent to you by HMRC when you register.
Agree with Bluebear about agreeing a Gross salary, will make your life a bit easier. Also try to do pay on a monthly basis, as then you only do the payroll run 12 times a year, not 52.
My suggestion would be to start doing it yourself, and if you really get very stuck, then contact a payroll agency to do it for you.