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.

Providing the specific context in clear and consise way is essential.

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.

That's a very good question. In my response, I am assuming that the question refers to an LLM-based chatbot.
From my experience, the best results are achieved the more context I provide to the LLM. This means providing as much information as possible that describes both the project itself and the project context.
A second very important step is the quality of the request, also known as the prompt for the LLM. This is similar to human communication, where the quality of the question determines the quality of the answer. Therefore, a good prompt strategy is required, for example:
1. Data and context about the project
2. The goal of the request
3. The task that the LLM should fulfill
4. The format in which the output should be delivered.

In subsequent requests, it is possible to build on the context and results of the previous request. It is important that this process takes place within a chat, as otherwise the context is lost.