If you are fitting a chimney pot and a liner see CHIMNEYS AND LINERS>flexi lining.
If there is an existing chimney pot in place then you will have to remove it. These things can be very heavy and you will need to take great care so as not to drop anything onto your roof or anywhere it may cause damage or injury to person.
I will generally use a lump hammer to break the old chimney, tapping it carefully so as to first cause stress cracks before breaking sections away. With particularly tall pots you can use an angle grinder and lop off top sections one at a time.
Note that pieces will likely fall down the chimney – what’s at the bottom to break or damage (make sure nobody is working within the fireplace)?
Using a breaker drill remove any unrequired or old and loose mortar flaunching from around the base of the old pot and then remove the last of the pot. You might not need to remove all or even any of the flaunching (I have removed a pot from its flaunching, like removing a loose tooth, dropping the new pot in its place).
If you do remove the flaunching you should see something like the pic on the left (in brick or stone). You should soon have a nice flat area now, a square or rectangle of bricks with the flue down the middle. Spread some mortar on this surface 3:1 mix sand/cement keeping it fairly wet. Many builders will now use peices of slate and place them as a base for the pot, making sure a decent sized hole is left in the middle (just a little smaller than the bottom of the pot). I have used 12mm concrete board and made a hole in the middle (make sure you PVA it). Make sure you do not make this hole smaller than the flue size required by your solid fuel requirements.
The pot will sit on the slate (or concrete board) on a bed of mortar.
Flaunch the mortar at 45 degrees so any water running down the outside of the pot has nowhere to collect.
Here’s a nice article with some pictures: