Perhaps the most basic way to add contacts on Messenger is through Facebook, itself.
Log into Facebook via Messenger, and then do a search for new friends using the Search field.
Once a friend has been added, they will automatically be added to your Messenger contacts list.
By Phone Number
Another method that you can use is to add a contact by their phone number. To do this, sign in to Facebook Messenger and select the People tab.
Next, tap the + button:
Enter the phone number of the user that you would like to add. Facebook will search for the user and give you the option to add them as a friend:
If the user is not yet active on Facebook Messenger, tap Invite them to join to send a chat invitation.
From Your Phone
Another way to add contacts to Messenger is to sync the application with your phone. Launch Messenger, and select the People tab. Then, press Sync contacts > OK.
You will need to give Messenger access to your contact list. Android users can do this by clicking Approve. iOS users will be redirected to their General Settings, where they can simply toggle the Contacts option ON.
Once the sync is complete, you will see a list of new contacts.