Easy access and regular joists
If your loft is easy to access and has no damp or condensation problems, it should be easy to insulate - you could even do it yourself.
If access is easy and your joists are regular, you can use rolls of mineral wool insulation. The first layer is laid between the joists - the horizontal beams that make up the 'floor' of the loft – then another layer is cross-laid at right angles to cover the joists and make the insulation up to the required depth. This can be done by a competent DIY-er or a professional installer.
Storage or living space
If you plan to use the loft or attic for storage, you will want to lay boards over the joists. Unfortunately, if you only insulate between the joists before doing this, the insulation won't be thick enough. To get enough insulation you can:
Insulate between the joists with mineral wool and then lay rigid insulation boards on top, with wooden boarding on top of that. You can buy insulation board pre-bonded to floor boarding to make the job easier. Or:
Raise the level of the floor so you can fit enough mineral wool beneath the new floor level.
Either way, make sure you don't squash the mineral wool when you fit the boards on top - this will reduce its insulation value.
If you want to use your loft for living space, you can insulate the roof of the loft instead of the floor by fixing rigid insulation boards between the roof rafters. Boards must be carefully cut to the right width so that they fit snugly between the rafters. They can then be covered by plasterboard.
Rafters aren't usually very deep, so to get the best performance you may have to insulate over them as well, using insulated plasterboard. If there isn't room to do this, make sure you use the highest performance insulation board available.
If your loft is hard to access, you can have blown insulation installed by a professional, who will use specialist equipment to blow loose, fire-retardant insulation material made of cellulose fibre or mineral wool into the loft. This doesn't usually take more than a few hours.
If your loft space is irregular, the joists are the wrong distance apart for rolls of mineral wool, or there are lots of obstructions that make laying matting tricky, you can use loose-fill insulation.
This is sold in bags as cork granules, vermiculite, mineral wool or cellulose fibre, which can be poured between the joists to the right depth. This can be done by a competent DIY-er or a professional installer: you may need to increase the height of the joists to get the insulation deep enough.