How do I determine what branch/tag I am on?
First, since Git 2.22 (Q2 2019), you have git branch --show-current which directly shows you your current checked out branch.
Second, it won't show anything if you are in a checked out worktree (created with git worktree add)
For that, check Git 2.23 (Q3 2019), with its "git branch --list" which learned to show branches that are checked out in other worktrees connected to the same repository prefixed with '+', similar to the way the currently checked out branch is shown
with '*' in front.
Example:

See commit 6e93814, commit ab31381, commit 2582083 (29 Apr 2019) by Nickolai Belakovski (``).
(Merged by Junio C Hamano -- gitster -- in commit 99eea64, 09 Jul 2019)
branch: add worktree info on verbose output
To display worktree path for refs checked out in a linked worktree
The git branch documentation now states:
The current branch will be highlighted in green and marked with an asterisk.
Any branches checked out in linked worktrees will be highlighted in cyan and marked with a plus sign.