Any "best" method depends, at least to a certain extent, on the project. Still, a proven, sensible way to begin eliciting the requirements for most projects is by interviewing the stakeholders and any subject matter experts.
A common approach to interviewing is to ask a list of prepared questions about a specific topic, compile the answers, and then begin sorting out the requirements. At other times, it may be better to kick off the interviews with a single broad question, and let the interviewee's answers shape the rest of the interview.
You can choose to conduct the interviews one-on-one, or in small groups of two or three stakeholders. Small-group interviews work best when the interviewees share knowledge about the same area of the project, or a set of common processes and/or needs. For larger groups, you might want to consider leading a requirements workshop—but that's another topic.