First you'll need to get your hands on some data. To make a map, you'll want some data with at least one column of accurate location data, as well as a few columns of other information.
The data.gov.uk site issues public data regularly and provides it in excel .xls format. It has an easy to use interface and it is searchable by many criteria. And because it's from the UK Government, it should be fairly reliable as a data source. It looks like this:
