Well, what do you want to know about the guy? Isn't this kind of individual? Ask about things that are important to you. Make sure you that if you have certain hang-ups you find out about if they apply to the guy. For example (and for example purposes only), if you have a thing against big noses, find out if he has a big nose. If you don't know what things are important to you, then I suggest you sit down and think a little bit, make yourself a list. Dating takes preparation, it's not just haphazard. The prepared dater has an easier time. Don't just go out with someone and see if it clicks. Find out before hand if he is all the things you're looking for in a husband.
Here's a skeletal outline of things that come to mind off the bat. To really ask about them though, you need to individualize these topics based on your personal preferences. So here are some basics: middos, life (learning/school/working) plans/goals, personality, religious background, family/individual medical/mental health/personal previous and present issues, hobbies/interests/recreational outlets, to what extent western society has a place in his life (texting/internet/tv/media/movies/secular music/etc), smoker/drinker vs. nonsmoker/drinker... (See, it already started to get hazy regarding what is important to the individual.)
Also, there are basic tactics to keep in mind when researching a guy, like don't let the person know what you'd prefer when asking a question because they'll usually try to tell you what you want to hear. So for example, instead of asking "Is he ambitious, or is he lazy?" Ask, "Is he the type that is always running from one thing to the next and gets a lot done, or is very thorough and takes care of things at his own pace?" You could also ask them to come up with answers instead of putting them in their mouth; it's usually very telling the first things they say. Example, instead of: "Would you say he's a mentsch, yaarei shamayim, and ben torah?" ask "What are 3 middos that come to mind when you think of him?"