It's a bit too lengthy and to discuss in detail here. The short version is: a) you file the petition for dissolution, b) serve it on the respondent, c) exchange financial information, and d) work out a settlement agreement.
2. As for cost, it varies greatly from case to case. If both parties agree on all or most issues, it can be as low as $1500-2500 while contested divorces can cost $15,000-$20,000+ per person. Other factors include hourly rate of the attorney which can range from $200-$600/hr., the efficiency of the attorney, the efficiency of the client, the complexity of the marital property, and whether the parties can cooperate in resolving the issues or fight about everything for the sake of fighting.
I would recommend consulting with an attorney. Many attorneys offer free or reduced-rate consultations. You would be able to get a more personalized and detailed answer there.