Chapter V., Manual for Courts-Martial (http://goo.gl/XPi4) contains the rules and regulations for imposition of Article 15 punishments, along with service regulations. You have the right to know the evidence against you, call available witnesses, make a presentation, have a personal representative with you, and appeal.
Article 15 punishments
Article 15 limits the type of punishment depending on your rank and the rank of the person imposing punishment. Generally punishments can include reduction in rank, forfeitures of pay, restriction to base, extra duty, and/or a letter of reprimand.
Article 15 appeals
You have a limited time to appeal an Article 15. They normally give 5 days to do that.
Article 15 and lawyers
Unless you are attached or embarked in a vessel you are allowed to get a lawyers advice on accepting an Article 15. You can do that with a military attorney, or for the more senior persons you can also hire a civilian attorney to help you.