You have to go and apply for it once your dependency visa has been stamped by Immigration border control.
Your wife will have to leave HK and return to get the stamp, then go to Immigration Tower and apply for an HKID card.
lets make it more clear for you and hope below info helps.
1. Once dependent visa is approved, your wife will need to activate the visa which mean she will need to leave HK and come back in, easiest way to do it is go to Macau and back.
2. Once she returns to HK and the dependent visa is activated, she needs to go apply for HK ID card.
3. Either go to HK Immigration tower early or book online http://www.gov.hk/en/residents/immig...kregidcard.htm
4. once you have the date sorted out, Immigration will take digital photos, finger print scan will be taken and fill out an application form. 1st time application if FREEEEEEEE
5. Process takes 30-60 mins in total.
6. She will be given a temporary paper ID CARD and a date when to pick up the real one which is usually a few weeks later.
more details here on how to register for a HK ID card and what documents to bring.
http://www.gov.hk/en/residents/immig...kic/appu18.htm
When your wife gets her dependant visa and leaves Hong Kong, before she reenters she has to apply for an Exit Endorsement from her local Public Security Bureau in Shenzhen (assuming her Hukou is in SZ). This takes about two weeks after she gets her visa and she won't be able to use the visa until she gets the Exit Endorsement put into her China to HK passport.
The temporary ID is legal to use though so dont worry about her not having the plastic one in time.
Edit: I mean in the mean time before the proper one arrives (takes a few weeks)