Click on the 'Add People' icon at the top of the board to add team members and guests.
Start typing a name or email and, if you’ve shared something with them before, their name will pop up. If not, you can send it to a new email (or ten) and the system will store them for next time.
Choosing a role
If you invite somebody who hasn't been invited to your workspace already, you’ll see this dialogue pop up.
New invitees are assigned a 'Guest' role by default, which means they only have access to boards they're invited to by team members. If you change their role to 'Team Member', they'll be able to view & join team boards without being invited, and can create their own boards.
Being a guest or a team member doesn't really affect what they can do on the board itself, it just limits what they'll be able to see and do within your workspace. If you want someone to be able to review the board (comment, star, etc) but not change it, it's better to use the 'Share for review' feature.