Its great that you've started the process to transfer your domain to us. If everything goes well, you should get an email from either/both of the following companies: Your Previous Domain Registrar, confirming that you are moving the domain away from them, and NameCheap, who we use to resell Domain names, confirming that the domain is moving to our reseller account with them.
There will be a link in one of the emails asking you to confirm the transfer. Please click the link to finalize the domain transfer.
Once you have clicked the link the final transfer will take place, this can be as fast as 1 hour to 12 hours, depending on the sending party. Please check your account page, which will reflect these changes once the domain has been transferred over.
When the domain is successfully transferred over, please confirm that the Name Servers match your account, as some providers (most notably GoDaddy) will reset your Name Servers before releasing the domain.
If you should have any questions, please feel free to contact support.