Watch several videos on how to replace a broken door latch. The videos were all helpful, but there was one that was a extremely help which greatly simplified installation. However, the videos all explained how to replace a broken door latch with a broken spring.
My spring was intact and only the tip of the plastic was broken. Replacing the new plastic piece was very difficult stretching the spring far enough to insert the plastic latch into that two slots.
After about 30 minutes, I said a little prayer asking my guardian for help and almost instantly the plastic hooks slipped into the appropriate slots. Doing the job myself saved me a lot of money.