Your question brings up two separate concerns:
1. The process for your wife
2. To what extent the Embassy will examine/review the previous filing that your wife went through based on her first marriage
With regard to the process for your wife, the process is relatively straightforward:
a. File I-130 with USCIS along with the fee ($420), proof of your US Citizenship, marriage certificate, divcorce decree(s), passport photos of each of you, G-325A for each of you and any documents that demonstrate that your marriage is bona fide (i.e. not just for her to obtain permanent residency)
b. Upon approval, the case will be sent to the National Visa Center (NVC), where another fee is paid and forms/documents are collecte (http://travel.state.gov/visa/immigrants/nvc/nvc_1335.html)
c. Upon completion by NVC of review of all documents, the case is scheduled for an appointment at the Consulate in Nairobi
This leads to the concerns regarding the prior marriage:
The Consular Officer (this might even come up at the stage when USCIS is making a decision on the I-130) might want evidence that your wife's marriage to her first husband was likewise bona fide. If not, there is a law (204(c)) that says any previous fraudulent marriage will result in any future petition being denied. Therefore, your wife and you willl want to put together evidence to clearly show that the marriage was legitimate. The Consulate is Nairobi is one of the toughest in the world on finding that marriages are fraudulent. I see dozens of cases each year where the spouse goes to Nairobi and is denied on a finding of marriage fraud. This results in the case being sent back to USCIS for revocation. While you would have the opportunity to challenge the findings of the Consulate on marriage fraud, it can take more than a year to deal with the revocation. I would plan carefully and consider hiring an experienced attorney under the circumstances.
Answered on Jan 16th, 2013 at 10:49 AM