If you know your friend's gamertag or you already have them on your Friends list, you can invite them to play on your realm directly! To invite a friend to play on your Realm using their gamertag, follow these instructions:

1. In Minecraft, select Play.
2. Select the Edit button next to the Realm you want to invite your friend to.
3. Select the Members button.
4. If you are not already friends, select the Find friends button. Enter your friend's gamertag into the field and press Enter. Select the Add Friend button. If you are already friends with the person you want to invite, skip to the next step. 
5. Select the Invite button next to your friend's gamertag on your Friends list.