So yesterday I heard back from a representative of the DAR. Apparently I have to choose a chapter first, then the real process begins (which seems a bit backwards to me, but oh well). Since I have a relative/ancestor listed in the DAR Patriot Index, hopefully there is paperwork already in place (from some other member of the family who's already done all the research!) so I can skip over the hard parts, which is proving lineal descent from one George Spangler.