We use PayPal for processing online transactions.
PayPal is a third-party company that was founded in 1998 to facilitate secure transactions over the internet. Today, it is used by about 35 million people across 100,000 sites in Europe alone, making it the second most popular choice for online transactions (after Visa)
Another very important aspect is security. PayPal uses the highest level of encryption commerically available, as well as numerous other measures. For more information, see also their security centre and buying safely pages.
Although transactions are easier if you have a PayPal account, PayPal are still perfectly happy to accept payments by card from people who don't have an account, without requiring them to create one.
Sources and further information: