Quick diagnosis: It seems your rhododendron hasn't been pruned lately... if at all :-) and that is fine. However, you can see that at the moment it looks like your rhododendron is bending over, mostly to the right (I believe that is connected to the source of sunlight which seems to be coming from that direction), and sending long "arms" that produce mostly leaves up, leaving the lower part quite empty.
What would you like to achieve? It's just like you wrote, I assume you would like your shrub to grow new leaves and fill out in the center. This is also an opportunity to rebuild your rhododendron, reduce the weight on the right hand side, and encourage new mid-height growth - but we'll do all that step by step, not all at once.
So let's prune...
Just before pulling out your samurai sword, allow the new bloom to complete its cycle - see those small soon to become flowers on top of the canopy? - enjoy it, and then unleash your sword (just don't forget to remove the Christmas lights off the shrub before you star cutting).
Begin by cutting off all the dry grey colored branches. Cut those as close as you can to their mother stem.
On the picture I have marked the following:
Red lines - mark the branches you should remove
Green lines - mark the cutting point, and of course whenever you see a dead branch feel free to cut it off as well.
When to prune? best time would be spring, summer as well. but avoid pruning during winter.
Scroll down for next pruning stage...
Again, the red marks show the branches that should be removed, in order to allow more sunlight into the center of the shrub (always good for rhododendron).
Green lines - these show the cutting points. I would like to encourage new growth around the cutting points. This will allow us to achieve your goal of filling in the shrub.
Now let's move on to the final cut...
Just kidding, you're done for the moment :-).
Remember that rhododendron is a very slow grower so don't expect quick results. I have no idea regarding your watering regime, but give him plenty of water soon after you've cut.
Also, these pruning instructions were very specific, because I don't want you to cut it all back. That's why I decided to leave some large branches with lots of leaves on them. Let's see how it responds this season and continue our work next season. I'll be happy to be kept updated.I hope that was helpful.
Providing general guidelines on 'how to prune' any kind of plant is important, but there are plants, and there is YOUR plant. So despite there being loads of information on this site, I also provide specific and personalized support. If something wasn't clear, or you're not sure of your plant's name, simply send me a picture with your question. Use the form below and I'll get back to you. In the mean time, see what others are asking.