You can check this article to learn about the domain transfer procedure and the problems that may occur.
Step-by-step guide

Steps to be followed while transferring domain from Customer side :

The domain registered must be 60 days old with current Registrar to transfer domain to new Registrar.
The domain must be unlocked contacting his current Registrar.
Get the EPP code for his domain.
Disable whois protection if enabled.

Domain Transfer process :

We accept the domain transfer and transfer authorization email will be sent to administrator ie. domain owner.
Once he approves the link the domain transfer will initiate.
Next step would be domain transfer approval from current Registrar.
Once it is approved domain transfer will complete in 5 to 6 days.


Problems that may occur :

If the domain is unlocked, Domain transfer Status will be: "Pending" .
If domain WHOIS protection is not disabled, transfer authorization emails will be sent to WHOIS protection email and not to the customer.
Sometimes EPP code issue may occur, so we have to get it again from the customer.
Current Registrar approval may delay and we can suggest customer to consult with them. (This can be done If customer asks for update and domain transfer status is: "Current Registrar approval pending")

If a customer asks why his domain still has the status: "Pending transfer", we should check the status of the domain transfer in Registrar panel and proceed accordingly.