Congratulations on the Gruen c_kelly!
Replacing hairsprings can bit tricky at first.
I usually use a tweezer and tiny brass pin. Laying the balance cock down on the bench and holding the balance with the tweezer, position it so that the hairspring falls between the index pins with the stud directly over the hole. You can then guide and push the stud in place with the pin in your other hand. The pin is small enough not to obstruct your view. I also use a pin when I put the balance into the movement and then place the balance cock over the balance (which is the way I usually do it). If you line it up correctly you can tap the stud with the pin until it begins to work itself into the hole. You can then use the tweezers to squeeze and set its depth into the hole. If you do it this way be very careful NOT to allow the balance to fall over after the hairspring is between the index pins as this will twist and bend the hairspring.
Hope this helps,