Gosh - tailpiece changes. They don't happen very often.
When you slacken the strings, you have to be careful that the soundpost does not shift. The tension in the strings holds the bridge down hard on the belly. That traps the soundpost between belly and back.
Actually, on some not-so-good instruments, the soundpost is jammed in so it's not a great risk of falling over if the strings are slackened, but you can never be too careful.......
Anyway, here's what to do (or at least what I did when I last changed my tailpiece):
Take off the chinrest
Get the new tailpiece at hand - and ready (that means having a big enough loop of gut to go over the black nobby bit near where you neck goes).
Hold the violin between fingers and thumb - thumb on the belly near the bridge, and fingers on the back underneath. Press to retain the soundpost in place.
Slacken the strings just enough that you can slip the old tailpiece off the nobby black bit near where your neck goes. The bridge will just fall over.
With one hand, still, try to get the strings out of the old tailpiece, and try to get them into the new one. If you can be very still, place the fiddle down somewhere, and use your other hand.
When the strings are in the tailpiece holes again, hold the violin firmly again, and get the tailpiece onto the black nobby bit. Then tighten the strings, enough to keep the tailpiece on the nobby bit, but not massively.
Slot the bridge back where it was (there will be marks from the feet). Make sure the bridge is perpendicular to the belly. It should not lean back towards the tailpiece or forward towards the fingerboard.
Tighten strings apropriately. (Sorry John - it's all that tuning again).
As the gut of the new tailpiece stretches, you will need to keep tightening the strings. All will go flat. (It's not quite as bad as new pirastoro strings....
)
Keep you violin somewhere where the temperature is around coolish room temperature, and it needs to be not too dry. I used to put a pot of water near my violin case, but that really is a bit unnecessary if you have a well ventilated house.
Hope that helps!
Tommo