My great grandfather on my mother’s side came over from Denmark in 1906 so my research quickly requires someone that speaks and reads a different language, as well as knows the system for vital records for a different country.How do you connect with someone who can do all that? I tried through Ancestry.com and also local universities thinking they might have a Danish language department that can point me to someone but finding someone who is fluent in Danish, let alone also knows the Danish vital records system, seems impossible.
Finding a specific professional genealogist may seem difficult, but there are a number of qualified people out there, but as you note, the trick is how to find them. We can suggest a number of different ways to find you Danish professional.
First, I would recommend the Association of Professional Genealogists or APG. You can search their website for genealogists who specialize in Danish research. In a recent search, I found over twenty professional genealogists who were doing Danish research. You might also want to contact Progenealogists.com, this company is owned by Ancestry.com, but has the resources to provide Danish genealogical research.
I might also suggest the article, Hiring a Professional Genealogist Resource Guide in the FamilySearch Research Wiki for more general information.
I might also suggest that you use the FamilySearch Research Wiki to learn about doing Danish research yourself. You might start with the article Danish Research: Getting Started.
As for the translation problems, you might want to try using Google Translate. You can use this free program to translate individual words or whole webpages.