Advancing FASD Research, Prevention, and Services Act This bill reestablishes and expands programs for fetal alcohol spectrum disorders (FASD). The Department of Health and Human Services must establish a research agenda on FASD, facilitate and disseminate findings on public health surveillance and research to prevent FASD, and establish multiple grant programs. Depending on the specific grant program, eligible grantees may include states, tribes and tribal organizations, public and private nonprofits, and educational institutions. Among other purposes, the grants support research on the diagnosis, intervention, and prevention of FASD; expand and coordinate surveillance; and foster collaboration to provide integrated services to individuals with FASD. The bill also directs the Department of Education and the Department of Justice to develop and disseminate trainings and best practices related to FASD.