If vegetables are undercooked you can tell by the firmness and crunchiness of the vegetables.
When vegetables are undercooked the vegetables will be crunchy and firm and be hard to pierce with a fork or knife.
If the vegetables are firm and crunchy and hard to pierce with a fork or knife then they haven't softened enough and need further cooking.
When the vegetables are fully cooked they should be pretty soft and easily chewed and easily pierced through with a knife or fork.
For potatoes when you're boiling potatoes they should be able to be easily mashed even with a fork and if not they need further cooking.
The length of time to boil vegetables or steam vegetables depends on the vegetables.
However most vegetables take between 20 to 30 minutes to steam or boil.
Potatoes take around 30 minutes to boil for example.
When the vegetables are cooked, drain the vegetables and serve the vegetables at once.
If you want to serve the cooked vegetables later, plunge the cooked vegetables into cold water to stop them from cooking further.
Then cook the vegetables again very briefly in boiling water when you are ready to serve.