Before you continue with this guide, if you're able to pick the lock with a paper clip. Picking the lock should be attempted first, because it will avoid the following step where you damage the lock.

Bend the paper clip into an "L" shape and insert it through the key slot. Using the end of the paper clip, feel for one of the two large metal stubs on the sides of the latch mechanism, indicated by the arrow. From the center of the lock cylinder, reach forward a little to engage the stub.

Push the latch back far enough to open the door.

That the door is not spring-loaded, so you will have to apply pressure with the paper clip while pulling the door open.