Your insulation and airtightness strategy will have been worked out at this stage with your energy assessor. For both insulation and airtightness the trickiest bits of the installation tend to be at the junctions, between wall and roof, windows and cavity wall, etc., to avoid thermal bridging. Existing homes present the challenge of working with some unknowns, and you may need to revise the insulation and airtightness strategy once elements have been stripped back. 

The type of insulation you will have chosen will determine whether you can go DIY or have an installer come and do it for you. For products like EPS beads and spray foam, the manufacturers of the products will have installers they work with who have been trained in their application. Same goes for external wall insulation unless it is a board or batt type which needs to be installed concurrently with the building up of the brick/blockwork.  

Insulation that comes in boards or rolls can be bought off the shelf and can usually be installed on a DIY basis with attention to detail. These are usually installed in two layers to ensure there is overlap at the junctions. It cannot be overstated how important it is for insulation to be installed correctly as any gaps will negate most of the insulating effect. As a rule of thumb, rolls should be rolled out loose, i.e. do not compact them, and boards must join neatly with no gaps (otherwise this can lead to thermal looping in walls for example). Always check the certification documents and manufacturer instructions on how to use their product effectively.