4. Keep the speaker (and yourself) comfortable and happy.
No one thinks well when they are uncomfortable–physically, mentally, or otherwise. If your consultant is coming to your space, take the time to make sure it is as comfortable as possible (this will mean different things depending on whether you are working in an air-conditioned office, in the field, etc.); that you and your consultant have access to water, etc., if appropriate; etc.
When it comes to mental comfort, keep in mind that your consultant is (a) almost certainly not a linguist; (b) probably not familiar with grammatical terms (even the ones you think are “simple”); (c) possibly uncomfortable making decisions about what is “right” in their language; (d) possibly uncomfortable producing marginally grammatical (or pragmatically odd, or socially odd) sentences; (e) possibly nervous about how they sound/come off/appear to you; (f) possibly nervous about the whole process. Given this, it is nearly always helpful to explain the basics of any part of the process as it happens (or before it happens). For example: explain how the digital recorder works; show how the speaker can stop it if they need to (if appropriate). Explain (in very general terms) what kind of sounds/words/sentences you are interested in.
If you can, and if appropriate, use authentic people/place names. This will help your consultant get into/stay in the mode of the target language.
Finally, know when to stop. It’s tempting to keep an elicitation session going for too long, especially when you’re getting a lot of interesting data. But remember, your consultant is above all a person, not a data-generator, and people get tired. If the speaker is tired, the data will suffer, and the speaker may be less inclined to participate in the future. Make sure you’re not too tired, either–if you are, you may miss important signals from your consultant.