When washing polyester in the washing machine the cycle you wash the polyester on is the normal wash cycle.
Use cold or warm water to wash the polyester and it will be just fine.
Do not wash the polyester in hot water as it may damage the polyester fabric but cold or warm water is fine to wash the polyester in.
The best laundry detergent to use for washing polyester is Laundress Signature Detergent which is what I use for polyester but you can use other detergents as well.
But I find the Laundress Signature Detergent works best for me when washing Polyester fabric.
Polyester does not shrink in the dryer under normal heat drying conditions.
Polyester is a man made fabric made of plastic and it is very hard to get polyester to shrink by accident so it's safe to dry polyester in the dryer without worry about the polyester shrinking.
The Polyester fabric is made of man-made polymer, which makes the fibers synthetic when makes the polymer fabric resistant to shrinkage.
However if you really want to shrink polyester it can be done by boiling some water and then you can dip the polyester fabric into the boiling water for a minute or so which will usually shrink the polyester.
I've done this before when I wanted to shrink polyester and dipping the polyester in boiling water for a minute started shrinking the polyester.