Decide if you can agree enough to use a single divorce lawyer together or if you each want separate lawyers. You can change your mind later, but if you have both shared too much information with the lawyer upfront he will probably need to withdraw. (Most lawyers moan like a drain when this happens. Please ignore them.)
Assuming you will each have separate lawyers you should approach a divorce lawyer who will issue a summons. Basically its just a legal notice that gets personally served on the other party by the sheriff. Your spouse then has 20 days for his or her lawyer to respond if they are contesting the divorce.
If the other party is going to be contesting the divorce then your lawyer will apply for a trial date which can easily be up to year in the future. The trial itself will be a full blown trial
If the other party isn’t going to contest then you would typically have the attorneys on both sides arrange some kind of settlement which will take a short while. After that the attorneys will have the divorce finalised by the court. Because it’s an unopposed matter this can usually be finished in a few weeks.