1) You can earn them by being active on the site. There is a full list of credit-earning opportunities on the Credts FAQ page. This is Muggy's preferred method.
2) Someone can give you credits. All members can transfer credits to their friends, but visiting their Manage Credits page.
3) An admin can give you credits. If you've been especially helpful around the site or win a contest, the site admin may choose to award you with any number of credits.
4) You can purchase credits. If you'd like to send out a bunch of gifts to your friends and don't have enough credits to do so, you can purchase them with cash. answerMug uses PayPal to handle the transaction, so your data is secured by them and answerMug never receives any of your financial info. We'd really prefer that you earn them, but if you want to buy them, the funds go to site upkeep and development, which is super cool. You can purchasse them on your Manage Credits page.