Use
your discretion. Is the web site from a reputable company, e.g. one
you have heard of before or one that has "real" outlets?
If so, they have their reputation to uphold and will do everything
they can to keep your details secure.
Does the site have a secure area for online transactions? To find
out, go into the page where you fill in your credit card details.
If there is a locked padlock on the grey bar at the bottom of your
browser window, the site is secure.
This means that the information you send will be "encrypted"
digitally scrambled with a secret code so that only
the online store will be able to understand it. Yes, it is technically
possible for someone to intercept this data and crack the code,
but really it is highly unlikely.
Lets put it in perspective
sending your credit card
details over the Internet is probably less risky than filling in
a credit card slip in a store which someone could look at
over your shoulder, or remove from the counter.