In order to create a custom Skype ID, you need to have a custom e-mail address.
For example, if you have an e-mail address like "email@example.com" the chances of you having a Skype ID like live:john123456 is very high. But if you create a more specific e-mail address like "firstname.lastname@example.org" you will get a Skype ID like live:john.smith
To do this, you have two options. You can choose which one that fits best for you.
Go to www.skype.com, click on "Sign in" and then select "New to Skype" (as in the image below).
Select "Use your email instead"
Select "Get a new email address"
You will create your new @outlook.com address
Add your first and last name that will show up whenever someone will search yo on Skype
And then you're all set!
You will be automatically logged into Skype for web. In order to find out your Skype ID, click on your name and it will be shown.