What will happen? - The spring will stretch.
How can I find the extension of the spring in this case? - Linear springs (I'm assuming yours is linear) obey Hook's law: F = -k*x. If you want to know how much force you need stretch the spring 5 cm (for example), you need to know the spring constant k. If you want to find the spring constant you need to measure how much force did you apply and how much did the spring stretch. If you want to know how much did the spring stretch, you need to know how much force did you applied and the spring constant.
The above wrongly assumed that F1 = F2. If F1 and F2 are different in magnitude then you wont have a system in equilibrium and you would effectively displacing the (already stretched spring) in the direction with the greater force.