Basically you cut it to fit tightly between the joists flush with the top. Don't rely on that to keep it in place, use nails into the joists below it to stop it dropping. You will either have to take up the whole floor or crawl underneath it (not my idea of fun). If you were keen you could nail battens to the sides of the joists to form ledges for the insulation to rest on. Make sure the void below is well ventilated. There should be air bricks at several places around the perimeter.  

re Cold bridging - Yes you are correct.  Don't worry too much about bridging. Just get as much insulation in there as possible. If you have any gaps between blocks of insulation or the joists just fill them with a _little_ expanding foam (comes in a can like squirty cream). Beware that it keeps expanding for some time so don't go mad with it. Try a little first and wait.

Sadly the Building Regulations require you to make a Building Contol Application when upgrading a thermal element such as a floor. It means you would need to put a certain  minimium amount of insulation in the floor.  This is covered by Part L which is horribly complicated...

http://www.planningportal.gov.uk/uploads/br/BR_PDF_ADL1B_2006.pdf

I believe the relevant data is in table 4. and that it requires floors to be upgraded to a U-Value of 0.25. However you may wish to do better than that.

Looking at the data on the Celotex web site (registration needed)...

http://www.celotex.co.uk/downloads.asp?i=25

it suggests you need around 90mm of Celotex to achieve a U-Value of 0.25.

For Jablite (modified polystyrene)..

http://www.jablite.co.uk/insulation/applications/jablite-Premium.php

I believe you need nearer 120mm thickness.

Edit: To be technically correct the thickness you need depends on the Perimeter/Area ratio eg long thin rooms need a different amount to short fat ones. Sorry this is all so technical.

http://www.secondsandco.co.uk/

The building regs specify minimium levels of insulation. Sadly some builders would cheat and not fit any if they could get away with it.

New thermal elements have to comply (See Section 49, page 22) as do upgrades to existing thermal elements (Section 54, page 23).  

Approved Document L1B: Conservation of fuel and power (Existing Dwellings)

http://www.planningportal.gov.uk/uploads/br/BR_PDF_ADL1B_2006.pdf

However reading it again I can't see where it says they are notifiable. Perhaps because it's classed as "Building Work".  Certainly LABC require an application to insert cavity wall insulation.