When using AI systems, what are some best practices for ensuring the results you receive are accurate, relevant, and aligned with your original goals?

A very good question and also difficult to answer as well. However you have to go to the basics and say as far as you are concerned, how well are you versed with the subject at hand ?. There are facts which the AI will generate and if you can verify these facts the more reliable the generated response will be. The fewer the facts then it means that the Generative AI response is far from meeting your original goals. Then it becomes very critical that you review the accuracy , relevancy and the alignment of the response to your original need. Unfortunately there are no clearly defined metrics that one can use a model to evaluate an AI generated response. So from my personal experience I basically restrict AI to an area where i have sound knowledge of , else it becomes almost impossible to verify details generated by an AI if you venture into unchartered territory. However with long usage and exposure your confidence also tend to increase as well.
The best practice  and protocol to follow  would be to consult subject matter expects  to validate the AI generated response before making critical decisions based on it to avoid any  inherent associated risks which you might be not aware of.

AI is a broader term. Generative AI is just an ancient model but everything "explode" when Google published the new architecture called transformer in 2017. So, with that said, take into account that generative AI is just "predictive test with steroids" just simplifying the model. With that said, two key points has to be taking into account when somebody works with AI: 1-human in the loop. 2-AI without Data (today called data science discipline or big data or whatever) is the same thing that live without oxygen. Talking about generative AI all related to technology has almost not impact with relation to all related to non-technological roles and activities. What you stated about accuracy and things like that are easy to implement because there are a lot inside disciplines like statistics. Most of them to make things "a priori" to prevent instead of cure. Few organizations taking into account that when generative AI environments are put in place almost a new business unit has to be created where roles like lawyers, linguistic, diversity and inclusion specialist must be hire to help on put it in place.

Like with any new tool, you need to test the results before you scale up.

Think about if you were to manually model a very complex problem in a spreadsheet. You don't build all the links and formulas first and then evaluate your final output. You build and test sections of the bigger solution first and then add on layers once you have validated the functionality.