One thing you will need is an SSL certificate. This basically protects the transaction from being "overheard". You can buy one from your hosting company and they aren't that expensive. Just a Quick SSL is enough but get it from an established provider like Thawte, Geotrust or Comodo. You will get less problems with browsers giving "Untrusted" notifications to customers but also it's more reassuring to see a "trusted" brand.
You should also look very seriously at your shopping cart to make sure it is fully up to date and patched and that you are using all recommended security settings. Think very carefully about securing those credit card numbers!
You might also want to look at security products like Sitelock or Truste. They are good for security but they are also very reassuring to your customers (I've seen studies showing that they bring in more money than they cost simply because customers trust you more).
Cheers - Tim from Ingenyes.