The first part of your court process with a DUI charge will be appearing in court for your arraignment. You will be given the option to hire a private attorney for representation but if you cannot afford an attorney, you may be eligible for a court-appointed public defender (or you may choose to represent yourself as it is your constitutional right).
You will be handed a copy of the formal charges being filed against you and occasionally the police report, and you will be asked how you plead: guilty, not guilty or no contest.
Finally, you will be given a date for your next court appearance where, in most cases, a plea bargain will be reached. If you chose to deny the plea bargain, your case will go to trial.
Make sure you appear at every court date for which you are scheduled.