To build Public Facilities just go to Public facilities in your build menu. With the exception of the monuments, who needs to be researched, they are available from the start. We recommend that you build public facilities only after you have done everything else and your company is stable, as they require a fair amount of money. Predictably, public facilities do not provide you with an income, but do add to your prestige, which plays a major role in supporting your political ambitions. Therefore, if you are planning to campaign for the mayoral seat in a city, it would be wise to build some public facilities even before you announce your candidacy. However, build was is within your means; if you are not currently seeking the mayor's seat, the research you do in your different headquarters might give you all the prestige you need.
In order to attract people to their cities, some might be tempted to build hospitals and other big public facilities, but the best thing to do is let the mayor himself build them. When it comes to health coverage, things can be very expensive. However, if the mayor refuses, then you might not have a choice. Police and fire stations are far less expensive, but you still should try the mayor first. As an apprentice, you should concentrate most on your survival and the stability of your company. Public facilities come later on, when you have money to spend. Parks are one of the choices, they are a very good investment, as far as public facilities go, you might consider putting them near your high residential buildings since they enjoy clean, green areas.
Public facilities may augment your prestige by 10 or even 20 points sometimes. Furthermore, they motivate other people to move into your town, because of the services and the beauty. The only drawback is that public facilities don't provide you with any direct income, and their benefits are shared by the entire vicinity or even the entire city. The mayor should really shoulder the burden of providing public facilities for the city, but in his absence the ideal would be that all the players share in the responsibility, dividing costs up amongst themselves. On a city level, the investment in public facilities is easily compensated by the overall economic health of the city.