The short answer to your question Dave - is with great difficulty.
Unless you are very lucky.
Been there and done that. The job was to simply remove old shower tray and fit a bigger new one without disturbing the old tiles. Sounds familiar?
On removal of the shower cubicle and tray I found out why it was leaking. The walls weren't square and the tray was out from the wall by nearly 20mm. Tubes of various Silicon and quadrant pieces had been used to cover this but without success.
Then there was the question of the waste, it needed to be realigned because of the new tray.
In the end we removed the affected plasterboard, built a new shower enclosure in 3 x 2 battens and green plasterboard about 3" out on both sides ( This made it easier to use different tiles by making it a feature and not have to worry about matching to poorly tiled walls). Reinforced floor with 18mm ply, resited waste and water inlet to shower and provided a trap door in kitchen (only way to do it) for access to trap and an isolation valve in case of emergency.
Sorry if this isn't what you wanted to hear but I hope you have better luck on a quick fix than I did. I can post some piuctures if of use
frogeye
