How do you thicken thinning grass in a shady area?

Apply a fertilizer for your type of grass at your locations proper time for application.

Is it possible to prune the trees in the area to allow more sunlight to reach the grass? You can also overseed the area (but stick to this method only once or twice a year). Good luck!

Grass needs a LOT of sunlight, full sun all day if possible. Thinning the tree to allow more light and seeding or sodding with a more shade-tolerant kind of grass will work if you MUST have lawn. I've done this with a live oak that literally covered my entire back yard. (Can you say bare dirt?)

In the alternative, may I suggest working with the shade instead of fighting it and giving up on grass altogether? There are many alternatives to a lawn you have to mow often. Create a beautiful, colorful bed with shade-loving plants like caladiums and elephant ear or even aspidistra (aka Iron Plant). Primroses will grow and bloom in part shade, too. You could even place paving stones and plant scottish or irish moss, then install seating for a relaxing area. Don't want to sit there? How about a sculpture garden with uplights? The possibilities are myriad!

Fertilzer, lime and shade grass seed.