We used a KD and we're just in the adoption process right now. We're in Ontario so this may/may not apply to you. Given that we didn't know what papers to file or how we went the lawyer route (and if anything went wrong we'd already have legal counsel in place). We were told it will cost us $1500-$2000.
1) Birth registration. At the time of birth, you complete the online registration for the birth of the baby (it's a 4 in 1 process, so you can also do birth certificate, SIN and child benefits at the same time). Because we used a known donor, only put the birth mother's name on the registration. Here's the form - http://www.ontario.ca/en/services_for_residents/STEL01_105212.
2) Birth certificates. Order the long form birth certificate in order to proceed with the adoption. It will take 15 business days from the time of registration to receive this document. We didn't order the short from birth certificate at this time because once the adoption is complete, we have to amend this paperwork, and re-order the certs with both of our names on them.
3) Second parent adoption. Each of the parties (you, your wife and your donor) will need to retain separate/independent legal counsel for the process and it is your wife who will initiate the adoption process (you and your KD don't need to meet with legal counsel prior to the paperwork being sent to them). Your wife's lawyer will draw up all of the paperwork and then send it on to your lawyer and your donor's lawyer. You and your donor meet with your respective lawyers and sign the papers giving consent for your wife to adopt. There is a 21 day waiting period where any of the three parties can withdraw your consent. After this time, but prior to the completion of the adoption, any of the three parties can withdraw consent by requesting that to the judge. At some point in time you get a court date (and I can't remember if this is right or not from our other adoption via CAS, but you do get the option to meet with the judge) and the adoption is finalized.
FWIW you can apparently get all of the paperwork from the courthouse and file on your own. It's just not easy to find out what paperwork you need and how to fill it out since our families aren't recognized on the form and the court apparently doesn't like too many amendments to their paperwork and has been known to reject the paperwork (according to our lawyer).
These second parent adoptions are not that common (our lawyer said she does 5 or so a year) and therefore not all lawyers are familiar with the process. I can let you know which lawyers we used in Ottawa and Toronto if that's helpful (our lawyers apparently work together frequently on these adoptions).