Generally, in a deposition, you are accompanied by your lawyer. A lawyer for the other parties is also present. The court reporter is present, transcribing all questions and answers. All parties have a right to attend the deposition, but usually, the lawyer appears on behalf of the party. Depositions are not typically public proceedings.
Generally, there is a broad and liberal standard for questioning at deposition. Anything that is relevant or likely to lead to something that is relevant is allowed.
The other lawyer is allowed to ask questions about your background, medical history, criminal history, work history, educational history, family make-up, other lawsuits, discussions with your treating doctors, and, of course, the incident at issue.
Certain topics are off-limits. For example, no questions are allowed about anything you spoke to us about, as that is protected by the attorney-client privilege.