First of all, I'm so sorry and my heart and prayers go out to you and your wife. We actually showed up to the hospital ready to deliver, they hooked my wife up to the monitors and the nurses were struggling to find a heart beat. Doctors were rushed over and the on duty doc told us he could hear heart flutterings and they needed to do an emergency c-section immediately or my wife would just deliver stillborn. Wife was whisked immediately away, put under and about 30 minutes later they brought my son out to me saying they tried to do everything. I then had to tell my wife --hardest and most devastating thing I've done.

A few thoughts in hindsight and going through it:
1) Just be there for your wife, love her because it's still emotional for to this day. What made matters worse was my wife had to recover in the maternity ward...so getting up to walk she had to hear and see new mothers.
2) Get pictures if possible and if baby looks good - we had 3 kids at the time and unfortunately this happened on my son's 7th birthday...but also fortunately because they'll always be linked. The hospital we went to had a volunteer who came into take pictures if we wanted. We didn't know...but I'm so glad we did. We put him in pajamas and had the kids hold him and take pictures. My 7 yr old son was helping the nurses take foot prints and hand prints.
3) We were surprised to see that vendors like headstone makers (yes it sucks that you have to even think about that let alone plan a funeral and buy a cemetary plot - which we also went along and bought for ourselves as well!) provide drastic discounts to stillborn. So check around. We made a bench and designed it ourselves at a fraction of the cost. Another vendor the hospital provided was of a lady that took the hand prints and footprints and took our other kids as well in clay. We have those keepsakes in our home to remember.
4) Don't be afraid to share your experience - everyone's different about how and what they want to share -- I decided to share and we received an outpouring of love and support - just as you're doing here. To this day, relationships are so much stronger because I shared and some came to our funeral, etc.
5) Get a priesthood blessing, regularly if needed, especially for your wife. And go to the temple (if you're a member), it provides a strong perspective, is a place you can feel your baby closer and just to be closer to your wife.
6) Share openly with your kids/family if you have those. My initial promptings I felt was that we are going to be so much stronger from this. This is not a club you want to be a part of, but my kids will always have this experience to look back on, to develop a testimony of eternal families, etc.
7) Get video and pictures to document the experience, ask your family kids about how they feel (if you want). We had a friend create a video for us for the funeral that included pictures of our baby, the outpouring of love we received from ward and neighborhood members, our kids, aunts, grandparents with the baby, etc. We now play that every birthday to remind us and celebrate.

These are just a few things we did, you don't have to do any, I just thought I'd share things that made a difference to us. Feel free to boardmail me for anything or if you just want to chat.