Citizens of EU member states and Switzerland can travel to the Republic with just their national identity card. Nationals of the UK have to carry a full passport (UK visitor passports are not acceptable) and all other nationalities must have a full valid passport. In Northern Cyprus, EU citizens can stay for up to three months.
You will need a valid passport to cross between the North and South. You’ll need to produce your passport or ID card every time you check into a hotel in Cyprus and when you conduct banking transactions.
Generally no restrictions for stays up to three months in the Republic and in Northern Cyprus.
General EU customs rules apply. You are allowed to bring in or out an unrestricted amount of (legal) goods, as long as they are for your own consumption.
Limits for entering or leaving Northern Cyprus:
The importation of agricultural products is subject to strict quarantine control and requires prior approval by the Ministry of Agriculture & Natural Resources.
When travelling, be aware that you become subject to both British and the Republic of Cyprus customs regulations when crossing passport control at Pergamos (Larnaka) and Agios Nikolaos (Famagusta), as those two checkpoints are in the Dekelia Sovereign Base Area (Great Britain). The regulations are the same, but it might take a bit more time.