This topic comes up regularly on these forums, churns a while and then goes dormant. It might be a candidate for a dedicated thread one day or a sticky. Until then, here are a collection of ideas gleaned from these forums which have worked in my system. That makes this anecdotal so YMMV when it comes to results in your system.
IMO (no more, no less) it seems to frequently be the case that there isn't one single thing that fixes the problem but rather attention to lots of small things that cumulatively make a substantial difference.
Use a dedicated center channel rather than a phantom center channel. A dedicated center will invariably do a better job and cover more seats in your listening space.
Finding and deploying a quality center channel will usually dictate how much you enjoy your home theater. Fortunately, there are lots of candidate speakers available with fans and detractors of each. Look for one that sounds natural and has good dispersion characteristics that cover the seats that are important in your home theater.
Carefully position all speakers, not just the center channel. A bad setup can create issues with dialog clarity. A good place to look for guidance is the Dolby web site here:
Avoid placing a center channel inside of a shelf or cubby since that can create reflections that degrade sound quality. A free-standing center channel below your display is often a good location, but some rooms accommodate that better than others.
Center channel location for best sound can collide with décor priorities. How this is addressed in each home theater depends on the parties involved in the decision. Try to err on the side of placement that gives then best center channel sound quality.
Try to eliminate obstructions between the listening positions and the center channel (e.g. tables, chairs, ottomans, etc.) since these can potentially degrade sound. If you aren't sure that there's an impact, try moving items out of the room one at a time and see if dialog clarity improves.
Verify that the center channel is aimed at ear level for the main listening position.
Consider judicious use of acoustic treatment for a room that's too lively.
Try removing the center channel grill to see if dialog clarity improves.
If your AVR / processor support it, be sure to configure speaker distance and size.
Try using the EQ system that comes with your AVR / processor. It can make a big difference in overall sound quality, including improvements in dialog clarity.
Check to see if your AVR / processor has the ability to increase center channel volume. Sometimes a dB or two can improve dialog clarity.
Experiment with Dolby Volume. It can potentially give a lift to dialog that's muddy.
Try lowering bass and increasing treble. It can improve dialog clarity with some material.
Recognize that there's going to be source material that just can't be rescued. It could well be the case that closed-caption is the best available option with really poor content.