Step 1 - Desensitize
Start with a medium sized, hard sided carrier that opens from the top and the front.
NOTE: Soft sided carriers are not cat friendly to cats who dislike carriers.
Make sure the carrier is very clean and smells fresh.
Remove the upper half of the carrier.
Remove the door.
Spritz a towel, kitty bed, or small blanket with pheromone spray and place in carrier.
Leave the carrier out where kitty has easy access to it at all times.
Do this for two weeks.
Step 2 - Positive Association with Food
Place a highly desirable food or treat at the entrance of the carrier.
Be sure to place the food when your cat is nearby so he sees you placing his favorite food or treat there.
Don't make a big deal of it. If he ignores it, that's okay. Just continue doing this twice daily.
Once your cat is eating the treats in front of the carrier, gradually place the treats further inside until the treats are eventually all the way in the back of the carrier.
After your cat has been comfortably eating treats in the back of the carrier, it's time to begin feeding him every meal in the back of the carrier.
Step 3 - Replace the Upper Half of the Carrier
Once your cat is comfortably eating in his carrier, it is time to place the upper half of the carrier back on.
Make sure to do this when the cat is not around.
Continue to feed your cat in the carrier.
Step 4 - Put the Carrier Door Back On
After 2-3 weeks of successfully feeding your cat all meals and treats in his carrier, it's time to put the door back on.
Make sure the door can't swing shut on the cat. Tape it open if needed.
Once your cat is very comfortable eating in the carrier with the door on and open, begin to gently close the door while he's eating.
DO NOT lock it or close it all the way.
IMPORTANT! If your cat becomes nervous or worried, open the door wide and allow him to leave the carrier if he wishes. This means your cat needs more time on the earlier steps.
Step 5 - Lock Door with Cat Inside
When you are able to gently shut the door while your cat is inside without any anxious or negative reaction, you may begin to lock the door while your cat eats.
Do this for just a few seconds the first few days.
If your cat shows any signs of distress, open the door immediately.
In a couple weeks or so, you will be able to leave the door closed for a few minutes after he has finished his food.
Step 6 - Moving the Carrier with Cat Inside
Once your cat feels comfortable locked inside the carrier for a few minutes, try picking up the carrier with your cat inside, then put it down, and open the door so he may exit if he chooses.
When your cat is very comfortable being picked up and put down while in the carrier, the next step is to pick the cat up while he's in the carrier, and carry him into another room.
Set the carrier down once in the room and open the door.
Your cat has now learned that the carrier is not a scary thing that only takes him to the vet!
Step 7 - Getting Used to the Car
Once your cat is comfortable sitting quietly in the carrier for 7-10 minutes, you're ready to try taking him out for a drive.
Be sure to add a soft, comfortable towel or blanket.
Encourage your cat into the carrier. If this is difficult, you will need to continue the previous steps longer.
In your vehicle, lay a folded blanket on the seat and place the carrier on top of it. This will reduce the vibration while you are driving.
Many cats travel better with a sheet over the carrier to block out direct sunlight, and also to block the view of things rushing by. Be sure to leave enough area exposed for ventilation.
Fasten the seatbelt around the carrier so it doesn't slide while driving.
Go for a brief drive down the road and back. Maybe just a minute or so.
If that goes well, go for a bit longer drive the next day.
Gradually increase the time as long as your cat is relaxed and comfortable during the drive.
Give kitty a treat once you bring the carrier inside and open the door.
Continue regular car rides over time, so that they come part of your cat's routine.
He will soon realize that most car rides are fun and only occasionally mean a trip to the vet!
References
This page had an excellent article on training cats to like their carrier - and we used most of their information in the above steps.