Pick wise your marriage counselor as you need to feel safe in his company in order to open and share the issues that brought you there. The more objective information you provide, the more helpful his advices could be so be honest and know that your conversations are confidentual, don't worry about leaking information about your personal life. It you don't feel comfortable on the first day of marriage counseling you may change the counselor with someone you fit easily (for example if you don't feel comfortable talking with a counselor from the other sex).
You should be open about your issues from the start. But don't unload your life story onto the therapist. He or she is usually the one who steers the conversation depending on the responses that you give to the questions that she asks. So like I said, be honest, say what you feel even if it might hurt your partner, but just watch how you say it.
The first time you see a marriage counselor, he or she will probably want to hear a little bit about your background and what kind of marital problems you’re dealing with. Prepare yourself to be completely candid about past relationships and any previous counseling experiences. Be yourself as much as possible, as it will help the counselor gain insight into the problematic relationship patterns you and your spouse are trying to overcome. Most importantly, be honest with yourself, your spouse and your counselor about how you are feeling. Then do your best to express those feelings without damaging the relationship.