A domain name transfer from a "loosing registrar" to a "gaining registrar" is a fairly simple procedure but it often could get a bit messy if you don't follow some small tricks with care.

The following are my recommended steps:

1. ensure that the contact info on your domain are correct. You can do so on your current registrar domain management panel (on the loosing registrar side). This is very important because you will often get a transfer authorization request at the contact email.

2. unlock your domain name. Most of the time registrars keep your domains in a "locked" status that protects them from accidental (or malicious) transfer/deletion by automatically forbidding any transfer request.

3. go to the registrar you want to transfer your domain to (the "gaining registrar") website and look for a "domain transfer" option. A domain strasfer procedure is initiated in a "pull" way, basically you tell the new registrar to ask for the domain transfer.

4. authorize the transfer. Usually you will get an email (at the contact address, hence why step 1 is important) from your old registrar (the loosing one) asking if you intend to authorize the transfer; you need to confirm this and the confirmation method depends on registrar/domain tld, most of the time it consists in copying an authorization code from the loosing registrar to the gaining one.

Hope this helps