Take a photo of the insides of the cassette box so it can guide when you are reassembling the cassette box.
Do not worry if you open the cassette box upside down (shown in 2nd photo) it is easy to correct; simply put the case back on, flip it over (shown in 3rd photo) and pull the new front side off (1st photo again).
Make sure all electrical circuitry and gears that were not removed are in their correct location.
Any other gears inside the cassette box, really aren't necessary. So feel free to remove them if the cassette is making too much noise (shown in 2nd photo).
Edit 3/14/2019: All cars are different. Many people in the comments have had luck keeping the center gears in the cassette and removing the interface gears. And also vice versa. Play around with it! If you can get it to work, awesome! If not, then try something else. Don't give up until you have your music playing in your car! Cheers!