An important criterion is the location of the area of your interest .
For temperate areas in the northern hemisphere, spring, summer, autumn, and winter are known to begin on the 1st of - March, June, September, and December, respectively. For temperate zone in the southern hemisphere, spring, summer, autumn, and winter are known to begin on the 1st of - September, December, March, and June, respectively. For a temperate region, the length of each season is approximately 3 months. In the same line (as an example), Australasian seasons: Summer, Autumn, Winter, and Spring are known to start (end) on 1 December (28 February), 1 March (31 May), 1 June (31 August), 1 September (30 November), respectively.
The seasonal variation for tropical areas is different from those of the temperate zones. Along the Equator, there are two rainy seasons March-April-May (MAM), and October-November-December (OND), and there are two dry seasons - June-July-August-September (JJAS), and January-February (JF). For areas with tropical climate (e.g. along or around the Tropics), the seasons are ONDJF, MAM, and JJAS (each letter is an initial of a month) and here, JJAS is a wet season.
To some latitudes it's common say Wet and Dry Seasons , because they haven't so good defined autumn and spring (next equator line). A good paper about this characterization you can find here:
I endorse the answer Charles Onyutha has given. It clearly explain the seasons in Northern and southern hemispheres in different months. If you have weather data, particularly temperatures and rainfall, you can analyze your self.
It is very simple that when you look at rainfall data, the start of rainy season you can identify by looking at slow and study increase of rainfall from a date in one month and continues till 2 to 3 months and then rain ceases. this you name it as rainy season in your area.