Please tell us where you're located (nearest big city, state) and the type of grass. Thanks!

Thank you @cecily 7A. I am in southwestern Ontario, clay based dirt (unfortunately) and I think the existing grass is just a standard sun/shade mix (fescue, etc).

Also, I have a gate in my fence backing onto a green park. I love to take the dog out this way, but the area around the gate is not only low lying, but all mucky. I'm thinking put sod here? Or use a premium grass seed (eg. Scotts Quick and Thick?)

Adding grass won't solve the wet area around the gate. That's going to need a swale to move the water elsewhere. Is there a convenient place for run off to be diverted?

Great idea. The end of the property (fence line) is the base of a small hill on the green space, which is problematic. Also, the property slopes (roughly) downward towards the corner of the property - this slope clearly needs to be properly addressed, making a "swale" and maybe adding river rock? Like in the picture from the internet? Perhaps I need professionals?

I've tried uploading 2 pictures and don't see them

Houzz is having difficulty with photos this week, it's not just you.

The size and design of your swale depend on how much water you're dealing with. Mine is a shallow depression slightly wider than our lawn mower that runs along the side of the lawn. It's wet in early spring then dries out until hurricane season. DH mows it during dry periods. Yours may need to be deeper with rock to prevent erosion.

Thanks a million! Would you hire a lawn service to do this (i.e. professionals)? I'm feeling a little intimidated on achieving the best look, although I am pretty handy and a workhorse, to boot.

Thanks so much for your great suggestions! Very much appreciated! (yes, Ontario, Canada).