In order to make outbound calls from your Exotel account, you need to submit your KYC docs here. As you would understand, these are for regulatory compliance. Once your have done it. they should be approved within a day and you will then be able to make outbound calls. Also, this FAQ page should help you understand what docs you need to upload.
Having said that, to allow testing outbound calls, we do allow calls to your verified users (in your Exotel account) without having to submit your KYC docs. For eg: Let say you add 2 users Swati and Chinmay. You can then login to Swati's Exotel account and make an outbound call to Chinmay's phone number (provided Chinmay has verified his phone number).
Making an outbound call
Keep the mobile phone/landline linked to your Exotel account close by
Click on the Call button on the top left, type in the number you want to call and press call again.
Exotel will first dial your number. Pick up the call. Wait while the number you want to call is dialed. When the person at the other end picks up, speak!
In case you're using the call API:
This page provides details of how to use Exotel's API to make outbound calls.
If you are a trial account you will see the following response when you try making an outbound call to number before you submit your KYC docs.
<Message>Your account is not yet KYC compliant. This is mandatory before making outbound calls.</Message>