Hello!  What I always do at first is I just open the coop/run door, and let them venture out (of course I'm watching, like you), and they're timid at first and usually hang right around the coop.  Usually running around and around, but staying close....then they get braver and braver.  
I usually don't start this  until they're very used to their coop and they've been in there a few weeks.  Then I start letting them roam the  yard.  I would just be very sure they can't squeeze through the fence....
I know you'll enjoy watching them run around in the grass.  Mine would run and flap their wings with such joy!  Like they were saying "Ahhhh Freedom"!
Now, it's a good idea to do this an hour or so before dark so that, if they don't automatically head back to the coop at dusk, you can catch them easier.  Chickens seem to calm down when it starts getting dark.  Watch and see......
Enjoy!
Sharon