People tend to speak more freely when unguarded. It is important that a business analyst adds a friendly tone to their elicitation meetings, a polite smile in agreement always helps.
One of the most common mistakes business analysts make in elicitations is draw the stakeholder’s attention to the contradictions in what they said. When you get conflicted facts from the same person, do not challenge the stakeholder, pretend you got confused to give them space to explain it better and correct their contradictions. If contradictions remain to identify that you need additional references for this piece of information, visit it later with the same stakeholder or with others but never confront a stakeholder of contradictory data as some will instantly classify you as a threat and this creates resistance to your mission on hand.
Understanding that a business analyst is a neutral facilitator without authority to judge, a certain position to defend or a particular solution to impose increases trust and collaboration with your stakeholders.
One of the most effective techniques in elicitation is eavesdropping, not in a malicious way! Eavesdropping is -in essence- similar to shadowing but without the formality of shadowing and observation. Listening to what business stakeholders say in lunch breaks, by the coffee machine and in social gatherings helps a business analyst not only analyze the stakeholders more thoroughly but also understand business facts in-depth.