If you have a lawyer representing you, whether it is somebody you hired or appointed counsel like the public defender, the attorney makes the ultimate decision whether to keep or excuse prospective jurors. Most lawyers ask the client for input -- especially in situations where the client is of a different race or ethnic group, and may be more aware of signs of prejudice displayed by potential jurors,
The attorney does all of the questioning during the voir dire process -- where the judge, then the lawyers, have an opportunity to ask questions of the potential jurors. The defendant is not allowed to address the potential jurors.
The only exception is a defendant who elects to represent himself. Before allowing a defendant to proceed without a lawyer, the judge takes a Faretta waiver, where the defendant is informed that he won't get any special breaks because he chooses to represent himself, he will be required to observe all rules of evidence and other court rules, he will be facing an experienced prosecutor, and it's almost always a bad idea to represent oneself.
Please understand that this is a general discussion of legal principles by a California lawyer and does not create an attorney/client relationship. It's impossible to give detailed, accurate advice based on a few sentences on a website (and you shouldn't provide too much specific information about your legal matter on a public forum like Avvo, anyway). You should always seek advice from an attorney licensed in your jurisdiction who can give you an informed opinion after reviewing all of the relevant information.
A defendant can always have a hand in picking some members of his own jury, or more accurately, in eliminating a certain number of jurors and leaving unobjectionable or less objectionable ones on the jury. Depending on the rules of the specific judge, a pool of jurors gets brought in the courtroom for each trial, and something called "voir dire" happens, where each juror announces their basic identifying information such as name, occupation, marital status, spouse's occupation, city of residence, kids, etc., and then the prosecution and the defense each get to ask the pool questions about their experiences, attitutudes, biases, etc. Then each side gets a chance to dismiss a number of prospective jurors without cause, called "peremptory" dismissals, as well as the chance to dismiss jurors if there's actual cause, like if someone announces that they're biased and can't be fair because of some past incident.
You can ask your lawyer or PD to explain this process to you.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
I agree with attorney Marshall's answer . To simplify, defendant only picks his own jury if Attorney let's him (but this never happens) - or if the defendant is representing himself. It's VERY important that the attorney use this time to build rapport with the jury - if he/she doesn't and the prosecutor does, the defense chance of winning goes way down.