Invite each person from Settings. It takes four steps, and step 3 is the one that lets them reply to contacts.
Send the Invite
Go to Settings → Team and click the + next to Team.
Enter the person's Email and choose a Role.
Turn on Add as Inbox Agent for anyone who will reply to contacts.
Click Send Email. They get an email to set up their name and password.
Don't skip step 3. A login only lets someone read the inbox. To reply to contacts they have to be an Inbox Agent, and that toggle makes them one as you invite them.
What each role can see is in the Roles section of the Settings guide.
If Something Goes Wrong
They can read the inbox but can't reply. They aren't an Inbox Agent yet. Add them in Settings → Inbox → Inbox Agents. The steps are in What Is an Inbox Agent?
The invite email never arrived. In Settings → Team, their row shows Pending Setup. Click Copy Account Creation Link and send them the link yourself.
You don't see Add as Inbox Agent. Every Inbox Agent seat on your plan is in use. Inbox Agent Seats in the Settings guide covers what each plan includes and how to add more.