Unable to edit a team board
If you're able to see your team's boards but not able to move or add cards, comment, or edit the board in any other way, you most likely aren't a member of that board yet. Being a team member allows you to see the boards and members that are part of that team, but it doesn't automatically give editing access to individual boards.
If the board's settings allow it, the quickest way to become a member of the board is to add yourself. To do that, open the board, and click on the "Show menu" link to open the board's menu (if it's not already open). Then, look for a "Join Board" button underneath the list of members. If you see that button, you can click on it to become a member of the board.
Click the "Join Board" button to add yourself to a team board.
If there's no "Join Board" button, you'll want to ask the board admin to add you to the board so that you can edit it. Not sure who the admin is? Look for the blue chevron in the corner of their avatar:
The blue chevron indicates the board admin.
Once you've been added as a member, you'll be able to make changes to the board.