There are mainly two reasons causing that Authorize.net payment method not showing in Magento checkout page
The Mage_Authorizenet and Mage_Payment module is not enabled
In Admin page, go to System->Configuration menu. In Advanced->Advanced section at left panel, enable the "Mage_Authorizenet" and "Mage_Payment" module.
The magento currency is not same as Authorize.net currency
Assume you are using US Dollar as your currency.
In Admin page go to System->Configuration menu. In General->Currency Setup section, set the Base Currency and Default Display Currency to "US Dollar". Then go to Sales->Payment Methods section, under Authorize.net (or Direct Post) tab, change the Accepted Currency to "US Dollar".