How can I allow third party to access Magento API? Can anyone provide brief description on this. I'm using Magento CE 1.7.
Any suggestion will be appreciated. Thanks in advanced.
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System > Configuration > Webservice and you will find the settings for Magento's APIs. Depending on what kind of API they want to use (SOAP-XML / REST) you can create a user for that kind of API and a role to go with it.
When creating the role I would advise you to be specific in what a third party can, and can not have access to. Only give permission to what is really necessary for them.
Magento has some pretty great documentation about their API's which you can find here