How should a Usability Test be approached?

This depends on the phase of the project and the goals that need to be set before. Every Usability Test needs to have a goal and then it is possible to start working on the tasks that should be fulfilled by the users. These tasks must be related to the elements that require evaluation as the users have to experience the solution so they can give feedback on the upsides and downsides after the usability test. The usability test setup can be completely different. If learning effects can come up for example the order of the tasks need to be switched between the usability test participants to avoid wrong outcomes.

Due to that effect one of the most common question is if a within subject or between subject study design will be chosen.

When makes a usability study sense?

A Usability Study can be done at any time and anywhere. Feedback from the users is the best feedback one can get. Whether it is on a low fidelity prototype or a high fidelity prototype does not matter as the feedback is always valuable. In a very early stage it might also be sensible to get an expert review as experienced UX Designers know the most common mistakes that were made in the past.