I would like to receive credit card payments for my business (tourist apartment). I actually get my guests via the booking.com website. This company provides me the guests' credit card details. But I don't have any POS equipment because it's very expensive to buy or rent one here (Cyprus). Are there any web-based companies that can do the process for me (I am sending the details, they make the processing, then transfer to my account)?
Yes, there are a bunch. I have used Paypal and it worked quite nicely. I see endless ads these days for Square, a tiny card reader that you plug into a smartphone that lets you swipe the card. (With Paypal you have to type in the credit card number.)