Please find advice on how to do this by selecting the platform on which you purchased Elite Dangerous.
Creating a Frontier account with Steam.
When you first start the game from Steam the launcher will pop up with this message as shown below: 
Click 'Create New Account' and you will be brought to a page where you will need to enter your account details: 
Fill out your details as shown on this form and click submit. If you receive the error message that a user with that email already exists, please use the Login button on the Existing Users section.
Please note, if you do not have access to Elite Dangerous through Steam, you will see a warning, (displayed on the screenshot above), which states you do not have the right Steam entitlements even if you register for an account.
If you find that this is the case, you may have access directly through your Frontier account, in which case, you can log into the launcher with your Frontier account details.
If you do have access to the game through Steam, this warning should not appear, in which case please continue with the steps below.
Once you have done this you will be brought to this page to confirm your email address. 
Once you have reached this page check the inbox of the email address that you submitted on this form, and you should find an email like this: 
On this email please click the link provided to confirm your account creation, once you are done you should be brought to a web page that will confirm your account has been created successfully and it will redirect you to the launcher. if you do not get redirected please open up the launcher again, and you should find that you are now logged in and able to click 'Play'!
Creating a Frontier account with Epic.
Please note that copies of Elite Dangerous purchased from the Epic Game Store MUST be run through the Epic launcher, as detailed in this FAQ. Linking your Frontier account to Steam will NOT add the game to Steam.
When you first start the game from the Epic Games Launcher, the Elite Dangerous launcher will pop up with this message as shown below: 
Click 'Link Account' and you will be brought to a page where you will need to enter your account details: 
Fill out your details as shown on this form and click submit. If you receive the error message that a user with that email already exists, please use the 'Login' button in the Existing Users section.
Once you have done this you will be brought to this page to confirm your email address. 
Once you have reached this page check the inbox of the email address that you submitted on this form, and you should find an email like this: 
On this email please click the link provided to confirm your account creation, once you are done you should be brought to a web page that will confirm your account has been created successfully and it will redirect you to the launcher. if you do not get redirected please open up the launcher again, and you should find that you are now logged in and able to click 'Play'!
If you experience any issues with this process, please do send in a ticket to our Customer Support Team by clicking the button below and the support team will be able to assist you further.