[SMHarman]

You need to choose your shoping cart software
Knowing this choose a payment gateway provider, Netbanx, Worldpay, HSBC, RBS, blah blah.
Set up your site on your server with your shopping cart software, for this you will need a host that supports the os and DB that your software runs on, most use MySQL and Linux so it's pretty easy to find one. King Phoenix Iweb solutions would be a good port of call.

Integrage your site with the payment gateway, you provide them with files for your checkout pages that they host on their secure server so your site passes the payment amount to their server, their server takes the card details and processes it and then confirms.

Unless you are planning to set up the next Amazon then this is the approach to take.

IWeb seem to offer HTTPS (or SSL - Secure Socket Layer)
Yes we can install an SSL certificate for you, there is an
installation charge of £15.
Or we can purchase one for you and install it this will entail a
yearly fee of £100

But the point of one of these is to integrate into a checkout and verify process. A point that will need a credit card authorisation agent anyway, pass the problem onto them, it's what they take their 2-8% for anyway.