Most dates apply to events or attributes. These are recorded in the Facts tab of the Property Box (see How to View an Individual's Record in the Property Box). Click on the event or attribute in question and the fields in the bottom half of the Facts tab will show more details about that event or attribute. The Date field is used to record date information about it. The date in question can be a simple date, or it can be a complex date. It can be an imprecise date or an estimated date. It can be a period (from some date, or to some date, or from one date to another). It can be a date range (before, after or between). It can be a Quarter Date. It can even be a phrase such as "2 weeks after his wife died", which can also be given an interpretation, if you wish.
To enter complex dates - not just for events and attributes, but for any date - double-click on the Date field, wherever you see it, or click on the button next to it, to open the Date Entry Assistant Dialog.