For all my trips to Cyprus I used Expedia's services in comparing and booking flights and hotels. Expedia website is very easy to use and contains an infinite number of holiday deals to practically any sunny destination across Europe.
On Expedia you can compare flights to Larnaca or Paphos, read detailed hotels reviews with complete photo sets and book your next holiday to Cyprus online.
If you're having trouble booking online, they also have a hotline that you can call and book via a phone representative. Bear in mind, though, that this is a costly expense as they charge you 10p/minute (might be more if you're not within the BT network). So my advise to you is to make the extra effort, book online & Save money.