As a mother of one and now pregnant with my second, I have some experience with this. I do want to mention that I AM NOT A DOCTOR, so please check any information with your wife's OB or midwife.
I breastfed my first until she was 14 months, and didn't get my period until she was over a year old. However, I never trusted breastfeeding as my contraceptive as it is not entirely reliable and I did not want any surprises. After my 6-week postpartum appointment, I requested a birth control pill (the pill is the only contraceptive that I had used). There is only one type of birth control pill you can take while nursing. This would be a progestin-only pill, sometimes called mini-pills. These do not affect milk production.
There are some other birth control methods that are considered safe for breastfeeding moms. Condoms, diaphragms, and spermicides would be fine. You and your wife may also want to research progestin-only implants (such as Norplant) and injectables (Depo-Provera). My OB recommended Mirena, an intrauterine contraceptive that can be left in place for up to 5 years, but removed when/if you decide to conceive again. I looked into this and was seriously considering it, but it wasn't covered as much as the pills and I knew that I'd want to have it removed within a year so we could try to conceive again.
I would suggest you and your wife talk to her OB or midwife to get more information on contraception. The OB or midwife will likely bring it up anyway at your wife's postpartum visit, but it's always good to do research ahead of time.
Good luck with the new arrival!