As a fellow GSP owner, as much exercise as possible and as much training as possible!!!
I found continual training classes for the first few years (we earned his CGC in the process!) was a great way for mental stimulation for the dog and establishing and maintaining the alpha position for the owner. This, along with as much exercise as you're able to give go a long way. I too have a fenced in yard with a doggie door. I think that is a necessity with a GSP.
I will say this, GSP's are EXTREMELY high energy and extremely inquisitive and are prone to one adventurous disaster after the next for the first few years. Around three years, I finally felt like I had some measure of control, LOL, and now at five years, he's the perfect dog.
My neighbor's 12 year old GSP still manages to get into mischievous trouble on a regular basis. They are eternal puppies. I'm lucky in that mine has a lazy streak.
But they are also one of the best dogs you could ever have! I adore this breed.