- Finding maps, importing them into My World GIS (or any other GIS you like). Be prepared for disappointment, guessing-and-checking. This is not a fun stage. Don't forget to use search tricks: advanced search, filetype: terms. Unfortunately, Google does not recognize filetype:shp the same way that it will recognize filetype:kml.
- Finding data, adding it to maps. (Note that you will need to demonstrate considerable prowess with spreadsheets and whatnot. However: I can help you solve any given problem you have at this stage; I just can't necessarily help you with the previous stage.)
Finding maps and data: Here are some resources to work with: https://delicious.com/tchammond/TLT394,dataSources. If you want country-level data, GapMinder.org is a particularly rich source. I can't imagine there's a better one-stop shop, particularly for historical info.
If you want to make life easy for yourself, just limit yourself to census data: https://delicious.com/tchammond/TLT394,dataSources,census. The Historical Census Browser from the University of Virginia, for example, is particularly easy to work with.
Keep in mind that you can satisfy the next assignment's requirement simply by playing with data -- you don't necessarily need to come up with an entirely new map. Just put new data on an old map, mash it around, and you're good. Depending on your topic, though, you may want to hunt down a new map or modify an existing map using the "Analyze" tab in My World.