This is how it works on my Sig, but yours may be different.
First, make sure the gun is unloaded. Clear chamber and remove mag.
When you push the release all the way in, you should see a tiny hole on the opposite side of the button. I use a straitened out paper clip to insert into that hole. This will separate the two sides of the release/catch. When you replace it, one side goes in first but I don't remember which (don't have the gun in front of me - I'm at work). You should be able to figure it out.
Did the gun not come with the owners manual? If not you should get one anyway.