From the dashboard view, tap on your workspace avatar (here the yellow circle written "AC") to open your workspace settings.
From there, tap to open the collaborator entry. The app displays the list of collaborators within your workspace.
Tap the "plus" button to add a new collaborator. Here, you simply need to provide you coworker's email address and the level of authorisation they should have on your workspace.
Tap the send button. They will receive an email inviting them to join your workspace. If they do not have a Sway account yet, they will be able to create their user and then accept the invitation.