Paste your chart. Pick a key. The words stay where they were.
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Your words stay where you put them, your tab stays tab, your notes to the drummer stay your notes to the drummer. The only other things that change are the key line and the capo line at the top, because if those said the old key the chart would be lying.
Put one on the 4th fret, play G shapes, and the band still hears B. So the line above your chart names both — the shapes in front of you, and the key you have to say out loud to everybody else. Take the capo off and the chords go back up by the same four frets.
Not A/B. The note under the bass player's hand moves too, and a lot of transposers forget. Sharps and flats follow the key you land in, as well: up one from D is E♭ major, so D/A comes back E♭/B♭ rather than D♯/A♯. Anything you spelled yourself is left exactly as you spelled it.