Using CiviCRM you can accept online card and PayPal payments for events and contributions. There is a wide and growing range of processors available but only a handful are actually distributed with CiviCRM. Check on the wiki at http://wiki.civicrm.org/confluence/display/CRMDOC/CiviContribute+Payment+Processor+Configuration or the extensions directory http://directory.civicrm.org/ to see whether the processor you need is available. There is also a forum board with information on community contributed processors at http://forum.civicrm.org/index.php?board=38.0. For many countries there aren't payment processors written that support their currencies while for others there is a choice. Paypal is the most widely available option. If you need to get integration with a particular payment processor, you might ask about this on the forums or approach one of the companies on the professional services page.
You can configure one or more Payment Processors for your CiviCRM installation. You will then need to assign an active Payment Processor to each Online Contribution Page and each paid Event. If no Payment Processors have been configured for your site, go to the New Payment Processor form Administer -> Configure -> Global Settings -> Payment Processors. On the Payment Processor form:
Choose Payment Processor Type from the drop-down list
Assign a descriptive Name to this processor configuration and an optional description. This is particularly important if you are configuring multiple merchant accounts for different chapters or sub-organizations within your site.
Make the processor active so it's available to events and contribution pages.
Finally fill in the details of you test and live accounts so you can use it in both test and live environments. You will of course need to do some further set up on the actual payment gateway but that is beyond the scop of this book and should be documented by your gateway.
Once you've done all that, the processor will be available in your paid events and contribution pages.