Cyprus is subtropical with hot summers and mild winters and has the warmest climate in the Mediterranean part of Europe, so technically you can visit Cyprus year round. The main tourist season in Cyprus is from April to October.
The best time to go would probably be spring (April/May), when temperatures are pleasant, crowds not as big and skies are blue. However, in this period the water temperature is still cool. Autumn is also nice with, although noticeably more hot and humid than spring, but the water temperature is great in that period.
Summers are from June-September and are hot and busy. Temperatures are between 22°C and 37°C. Being just off the coast of the Middle East, temperatures can be quite high, with its peak in August. Temperatures can go up to 40°C and rainfall is rare. Since this is also the busiest time of the year, avoid it if you can. During summer it would be wise to book an air-conditioned accommodation. Overall the north coast is slightly cooler than the rest of the island due to the mountain breezes from the Kyrenia Range.
Autumn (September/October) can still be hot. With rain falling mainly in this period (and in winter), it can be very humid as well. This can be a good period to go hiking in the mountainous areas.
Winter-time is quiet and much colder, especially in Troödos Massif that is covered with snow. Tto many it comes as surprise that you can even ski on Mt Olympus from January to mid-March. Water temperature: around 17°C-26°C (64-80°F) from May to July, rising to 26°C-28 °C (80-82 °F) in August/early September and dropping from 24°C to 17°C between October and December.