Corolla Handbrake

[TonyHSD]

There is no exactly a correct procedure and this will depend on where you park and what do you like to achieve. 

If you park on level ground no need to bother with parking brake at all, this is what I do often.

If the car is parked on incline and you want easy and quiet shift from P to R or D after restart the car the correct procedure is when you parked the car with brake pedal pressed shift to N , apply parking brake, release foot brake, the car will move slightly, select P and turn off the car. 
On your return when you start the car and select R or D it will be easy and quiet. Here remember that if the engine kicks in before you select R or D the initial engine start up can be accompanied by a thud, this is because of odd position of the planetary gear set , nothing to worry about it. 
If you parked on incline and select P, release foot brake, the car moves slightly then apply parking brake on your return the shifter will be stiff to move from P tomR or D since the weight of the car is loaded into transmission pole , however if the engine kicks in before shifting out of P there will be smooth start up and no thud. 
Either of these methods are used there is no risk breaking anything, or damage or anything unusual. 👍