Border Collies are a very active breed. Depending on age and activity level, I would say that your Border Collie could exercise until it can't run anymore!
At least an hour or more a day is what I would think would be appropriate.
Oh of course, as Angeleeta said, lots of exercise.
My neighbor has a Border Collie, excellent little guy - one year old. He plays with my cattle dog and they wear each other out; so it's great for both.
But I would agree with an hour atleast a day, running around would be best. Otherwise you might see problems.
Border Collies are herding dogs and they can be pretty intense. Keep in mind that they do best when they have a "job." They need more than just running around. They need to think too! Good things to do are throwing a frisbee, obedience training, agility, or just train a simple trick like "shake hands."
I just finished the book "A Dog Year" by John Katz, and regarding Border Collies, he had the best quip on the breed ever.
It's tough to meet or read about a Border Collie and not want one. They are beautiful, intelligent, storied dogs. Under certain conditions, you can have a wonderful relationship.
But acquiring a Border Collie can also be a major mistake, both for you and for a dog that looks great on cable shows but needs very particular circumstances in order to thrive.
Believe me when I say that this breed isn't for everybody. Border Collies need hours of exercise, they can be unpredictable around small kids, they are hyper, obsessive, territorial, and weird. If you don't provide continuous and challenging work and exercise for them, they will find ways to busy themselves, ways you probably won't appreciate.
There are lots of working dogs and other breeds, including happy and healthy shelter adoptees, hat are much easier to raise and far better suited to urban and suburban life.
If you are pondering brining a Border Collie or, for that matter, any other dog into your life, please consider it carefully and talk to breeders and other owners first.