There are 2 airports in Cyprus: Paphos interational airport which is about 25 minutes drive away and Larnaca International airport which is about 1 and half hour.
There are a number of airlines who fly to Cyprus - You can visit the follow websites:

www.ryanair.com
www.easyjet.com/en
www.cyprusairways.com/main/default.aspx
www.ba.com
www.xl.com

Outside from the airport you can find buses to get here. For more information you can visit the follow websites:
www.pafosbuses.com
www.airportsshuttlebus.eu
www.pameaerodromio.eu

If you interested to hire car please find below some websites:
www.paphoscarrentals.com
www.zandxcars.com/

Finally, Outside from the airport you can find taxi to get here.
( Rania 26964464)
or websites:
www.travelrepublic.co.uk/
www.taxipaphos.com/