There are several ways of adding new members to your team, and the most convenient one will depend on your role within your organization.
As a Team Owner:
Navigate the Teams tab within Teams Manager.
Find the desired team.
Click on the Member button at the bottom of the corresponding Team Card.
Write the name of the desired team member in the Manage users pop-up.
Click on add and close the pop-up.
As an Admin, you have the option to do this through the Dashboard as well:
Navigate to the Teams tab within Teams Manager.
Switch to Admin view from the top right corner.
Find the desired team in the Active tab.
Click on the … button and select Manage Members and Owners.
Team composition can be changed through the default Microsoft Teams menu as well, however, it's preferable that you stay within the app for the best possible experience.