To change your government type, you will have to instigate a revolution (these might also come along whether you wish it or not). When the population of one or both of the classes in a region gets angry (-1 or lower public order), they will go on strike/write complaint letters the first turn, riot the second and revolt the third if nothing has still been done. If this revolt happens in your nation's home region, it will become a revolution. When these occur, you will be given the choice of joining the revolutionaries or to stay loyal to your current government and keep your current form of government.
If the lower classes are the ones that starts the revolution, the result will be a Republic. If it's the middle classes, the result will be a Constitutional Monarchy. If it's the nobility, the result will be an Absolute Monarchy. Thus, if you want to go from an Absolute Monarchy to a Constitutional one, you will first have to angry the lower classes and become a Republic, then anger the middle classes to become a Constitutional Monarchy. If you are an Absolute Monarchy and you angry the nobility, you'll still be an Absolute Monarchy, but you'll get a new King or Queen.
Note that, as mentioned above, revolutions can only occur in your
home region. If the population in another region gets angry, this will not start a revolution but merely a revolt that you will have to squash before it spreads.
A few tips concerning revolutions is to move any troops out of your home region before they happen if you want to join the revolutionaries, or to move them into the capital if you want to join the current government. Troops in the capital will stay loyal to your current government. If you want to join the revolutionaries, it can also be a good idea to destroy any walls you might have built in your capital. To create a revolution more easily, you can crank up the taxes for the class you wish to start the revolution to max, while exempting all other troublesome regions than your capital from taxes, so that they don't revolt while you're occupied with your revolution.
While the country is in this state of revolution, the rest of your nation will be completely grayed out until the revolution is concluded, and nothing will happen in your other regions. Therefore make sure you end each revolution as quickly as possible