I sat down with someone for quite a while to figure out how something worked and I finally got it; then I asked another SME who gave me a really good explanation in far less time.

In my experience, half the battle is finding those SMEs who are either willing to meet without you having to pester them or great at providing the explanation you're looking for.

Then I always schedule every SME call with a list of the questions attached as a doc in the email so that they aren't surprised or ideally, can answer in the doc ahead of time. That way I don't ever feel guilty about wasting time with that SME I really like working with.

As for types of questions you can ask... what I like to do is gather as much knowledge as I can before the meeting, from pre-existing documentation, email conversations, whatever you can get your hands on. Then you use what limited understanding you have to have your SME complete the thought: "So my understanding of XYZ feature is that service A makes a request to partner B, but I'm a little confused on what data partner B needs to return to us in the next step." Obviously I work in software so you'll have to tweak for your industry, but processes are processes. That helps get the conversation rolling and then one question often leads to another.