Well, here's a visual example of how I usually panel longer, explain-y conversations:
Key strategies:
-Vary dialogue weight-- don't just do tons of big bubbles; mix in shorter phrases to give rhythm to the speech and avoid a 'lecturing' effect
-If you have to do headshots, make 'em expressive (and pretty~)
-Have characters act while they speak
-Break away from reality occasionally; do panels with images relevant to the convo
Although, if this...
...is happening to you a lot, you may just have an editing problem. =/ Like, at some point you have to remember that you're the writer, and all the things your characters 'need' to say are under your control.
Another thing you have to remember is that stories aren't real life. Even if, realistically, a conversation might go on for 30 minutes or 3 hours, if that's bad for your story's pacing (or for holding the interest of the reader...) then you need to cut it down. Get rid of things that aren't particularly interesting or informative in regards to the plot.
Although, that's assuming your goal with your comic is providing an entertaining experience...if you just want to play with the characters, editing does matter less...but don't be surprised if other people don't have as much fun just watching you make them talk. =/