I would strongly recommend starting off with a visit to the excellent Malta at War Museum in Birgu (Vittoriosa). This museum caters to families and experts alike and gives a great overview of the Second Great Siege of Malta with its fascinating displays. When visiting, make sure to explore its large underground shelter, which is a real eye opener.
Take time to walk around the Three Cities area. Here, a lot of buildings still have bomb damage with shrapnel marks on their facades. The Inquisitors Palace is a good example of this.
The Island was preparing itself for an invasion, so you should be looking out for pillboxes (concrete bunkers, which would have housed machine guns). These would have been found on the shoreline as a first line of defence and then further inshore in defence lines. Look out for them at junctions on hills etc.