You can send him an invite. On PC Just go to his/her city, click on the fellowship icon/banner and if that person is not in a FS you'll get an option to invite them. Then they have to accept the invite.
The other option is that they send you a request and then you go to your FS icon/banner and you look for the 4th tab - aspirants - and you find that persons request and let them join. I think you have to be mage to be able to see the "aspirants" tab though, or maybe at least ambassador, not sure.
If you are both playing on the mobile app, it will be nigh on impossible to find each other to send an invitation or application, unless one is within the explored map region of the other. In which case another player in your fs who is ambassador level or above and who plays on pc can search for them and send the invitation instead.