As has been pointed out the vapour barrier would provide a means for condensation so not good.
Measure your width between joists (don't assume they will be all the same, for some reason they can differ). Measure the total length you will need for each run.
Cut your insulation to width, plus a wee bit to give interference fit (it helps when installing). Now cut your length, BUT, limit this to say 2 metres. The reason for this is the manouvering in such a limited space, trying to take a length of say 4 meters down a hatch and offer it up in that space is just too problematic. OK, it will take longer but will be easier to manouver shorter lengths.
So at this point you have your piece cut to size.
Now bag it. This will make it easier to manouver when down below. Its all personal preference but if you fold it in half, put it in a large bag it can be dragged around down below without picking up all the crap/dust or whatever is lying around down there.
Once you have reached the area you can remove it from the bag while simultaniously pushing it up into position. The interference fit should help hold it there when doing this.
Now that's one possible way of doing it, and there may be others, it all depends on the situation and you personal preference.
Fitting in position :-
Where people have mentioned chicken wire, and indeed I have also mentioned it as an option, in this case i would suggest that trying to put up chicken wire would be darn near impossible due to the space constraints. Or at the very least just too difficult.
I would go for a "damp proof course" material on a roll, something like
screwfix 25271, 100mm wide.
It is placed at regular intervals along the "run" to provide support to the insulation. It can be stapled into position (stanley heavy duty staple gun
screwfix 62930).
If you choose this method, cut the material a bit wider than the joist width, staple up one end of the dpc material, push the insulation up between the joists, then you can staple the other end of the dpc material onto the joist, cut of the excess using a knife. This will hold the insulation up in place and allow air to circulate. Just leave space between each section of dpc material.
Yes, there are other methods/materials to use, this is just one option, final decision will be yours.
Safety/PPE
If you can afford it go for the best spec'd stuff you can get.
It is going to be a messy job with lots of dust and fibre floating in the air all the time your down there.
I personally wouldn't use the cheap white "dust masks" with the two bits of elastic.
Ideally I would say and use a full face mask but unless you have a need to use these on a regular basis then its prohibitively expensive (£120), or perhaps someone may be able to lend you one or ebay(?)
Perhaps a half face dust mask, 3m 4277 type. Better still are the ones with the removable cartridges (the masks can be kept for years and with a cartridge change every so often can be used on other jobs.
The beauty of these types is that they are made of a flexible silicone rubber which gives a good seal.
Obviously you'll want the best seal you can get and to my mind these are the only ones that cut it. Perhaps other people will have other ideas and point out alternatives.
Goggles - obviously (unless its a full face mask).
Gloves - marigolds or something similar.
Watch the seal between your hands and arms, otherwise your wrists will catch the fibres.
Paper suit - saves the dust/fibres clinging to your usual work clothes and can be thrown away after a few uses. Granted they can be delicate and will have to be used with care. Consider one with a hood.
And YES, it will be warm and sweaty work with all that stuff on but its essential stuff. (especially with all those fibres)
Lighting - a work light or two. Best to avoid those that give out a lot of heat.
May be a bit safer to use alternative insulation material but what has been written is written thinking about the fibreglass type of insulation.
It's a job for the short and skinny folk down below the joists.
That's not very PC is it?