Adding participants to an existing conversation follows the same flow as when you originally created the conversation.  In order to do this, you need to get to the "Conversation Details" screen.

1. From within any conversation, tap the Conversation Details icon in the upper right

2. Tap "Add Participants"

3. Select participants from the list or tap invite with a link. If inviting with a link, send it to the recipient(s) via text, email, etc.