If you have selected the Sign in with eID option on the EU Login homepage (ecas.ec.europa.eu/cas) instead of setting up your eID authentication method as described in below instructions and you face access issues, please refer to the following article: I linked my eID to another EU Login account and I cannot access my saved data anymore.
Instructions
Watch the video tutorial or access instructions illustrated step by step below the video.
Step-by-step
1. Connect your eID to your computer using a card reader first. Alternatively you may use a National eID mobile application e.g. ITSME for Belgian eID.

2. Go to the EU Login homepage (ecas.ec.europa.eu/cas).
Click on the arrow of the Choose your verification method drop-down list, select Password, then enter your password and select Sign in.

3. On the top right corner, click the Settings cogwheel icon next to your name and select My Account.

4. Click on Manage my eIDs.
Note: The system will request you a stronger authentication than password only if you already have one configured (e.g. the EU Login Mobile App).

5. Select Link my eID.
Note: You will be presented with all compatible eID countries' flags.

6. Select your country's flag and select Submit.
Note: If your country's flag is not in the list, this unfortunately means you will not be able to set this authentication method.

7. Follow the on-screen instructions as you are being redirected through the eIDAS website and your country's identity provider system to establish the link.
Once linked, your eID can be used from the very first EU Login screen, authenticating your directly with the two-factor authentication.
Any issues?
If you have selected the Sign in with eID option on the EU Login homepage (ecas.ec.europa.eu/cas) instead of setting up your eID authentication method as described in above instructions and you face access issues, please refer to the following article: I linked my eID to another EU Login account and I cannot access my saved data anymore.
More information and details
Consult the EU Login User Guide.