How to do Machine Learning the right way?
There is not really a "right way" to use machine learning outside of running the algorithms, any more than there is a "right way" to use a sorting algorithm, or any other kind of complex automation.

Some guidelines/thoughts:


You can start using your model to make predictions, once those predictions are useful to you. This may be once they pass some threshold in performance that would make the predictions the best way of achieving some other goal. That may just mean "better than the last ML model", but could also mean "cheaper and faster than having some people doing it, even if it is less accurate".
Depending on how your training data is collected, and how the model works, it may be possible to both use your model for predictions, and to continue training it on new data as it arrives.
However, there is no requirement for continuous learning. Learning systems that continuously adapt to new data are useful in some situations (example might be recommendation systems), but might be inappropriate in others (example might be automatic driver for a vehicle, where you don't want to risk reduction in performance whilst in use).


One thing that is considered very standard practice is to demonstrate how the machine learning system is performing after a period of learning by using a test metric. The simplest variation is to keep some of your precious data to one side, deliberately not training on it, then measure the performance. Often two such sets are kept aside - a cross validation set is used to help decide automatically between variations of your learning algorithm, and a test set is used to assess the end result of that selection.