Browse for the investment banks that deal in your state and contact them to discuss your scenario. You can go to JP Morgan, Merrill Lynch and Goldman Sachs etc. All these banks deal in the activity of Initial Public Offerings. Hence, you will have to contact them first before taking any step.
You need to start preparing the documents that you will show the bank at least a year before you want to go public. It is a long and hectic process. Therefore, you need to start working long before you will go public.
Assess the amount of Initial Public Offering with utmost care because it is a major decision and you will not be able to infuse more or suck some shares in or out of market respectively after an Initial Public Offering.
The bank that you have discussed the scenario in the first step will take your case to the Securities and Exchange Commission that will assess your application. Banks are good at their job so they will not get a negation in a response to their application.
After all the legal stuff is completed, the bank will ask you to give a date for the IPO and you will provide them according to your plan.
Bank will write the shares on your behalf and make them public on the day you decided in the previous step.