My friend wants me to be the adoptive parent. What steps should I take?

You both need lawyers; that is your first step.

Illinois does not require an adoptive parent to be married. So this can work if your friend wants to do it.

But I would urge you most strongly to have an attorney draw up the paperwork. Do shop around for an attorney in IL and then follow their advice.

1. Get an attorney specializing in adoptions.
2. Get your friend into counseling to deal with the emotions that go with choosing adoption.
3. Get yourself into counseling so that you understand a. Your motivations. b. Your friend's grief. And c. your (prospective) child's needs as an adoptee. Find someone that specializes in adoptive parent counseling.
4. Realize that adoption is HIGHLY emotionally charged, and that you will very likely be unable to remain friends with your friend after the adoption unless you spell out VERY clear and concise rules about contact in advance--and even then, it's chancy.