This is fairly a self-explanatory achievement though there are a couple of areas which can cause a little grief.
This cannot be won in the colonial era as you have no healthcare facilities. Lack of entertainment options will also give you an issue at this point.
To gauge happiness - hit
and then
once to cycle to the happiness section. Here your overall happiness will be listed.
The two causing most problems will be job satisfaction and housing.
Job satisfaction is linked to employment and happiness at work - this can simply be increased by paying more (increasing individual industries or building's budgets) and by paying for upgrades that increase workers' happiness. Installing a manager with this influence will also help.
Housing happiness is severely deflated by homelessness and to retain a high satisfaction you must avoid tenements (better than being homeless but only marginally). Also using the edict 'mortgage subsidies' will allow you to build mansions and other higher class homes which are then made accessible to poor and less wealthy people.
Increasing the budget of individual houses will also increase the happiness.