the child tax credit is calculated on form 2441 and filed with your tax return, the percentage is based on your income... the more money you make, the smaller the percentage gets. the nice thing is that it is a tax credit... not a deduction. so for every dollar of the credit, that is a dollar less in tax you pay. granted it is not dollar for dollar with what you spend, but it is a pretty nice benefit.
you DO need the providers name, address AND social security number... this is provided on form W-10 as someone else has posted and despite what others have said, if you do not include this information you may receive a tax notice for an incomplete form and the credit can be disallowed... also, you can't claim child care as an other business expense... it would not qualify for someone who is self-employed nor as as other itemized deduction. get your facts from your cpa!
also, if you had a nanny who came to your home and provided childcare that is when you run in to the possibility of being subject to paying payroll taxes... typically it is when you pay someone more than $1000 in any calendar quarter... which exempts most "casual" babysitters.
someone outside your home that provides childcare independently is responsible for properly reporting their income earned from such activities... yes, a lot of people work under the table... but it is still illegal to do so... I realize it doesn't pay that well, but it is still tax evasion.
however, you have to communicate the expectations of reporting or not reporting income up front.. and you may lose convenience and friendship if you decide to push the issue of claiming the deduction. also, this could cause problems for her as the irs can match up your information and hers... and she may be found out that she is working under the table.
anyway, it can be a sticky mess... personally, I have to pay taxes on what I earn... and it kind of gripes me that other people feel like they don't have to... though by the same token, I can understand why people are tempted to keep things off the radar.