How to come to Africa from Europe?

Take the train?

Train and/or boat seem to me to be the cheapest solutions other then hitch-hiking.
You could go to Venice by train (or to any port in Croatia that offers ferry services) and from there take a ferry.
Depending on where in Africa you want to end up, you can do a search on internet with the words: ferry, italy, libya (for example) or greece, ferry, tunisia.

Can you be a bit more specific?

The place is millions of square miles.

If you want to go to Morocco, for example, you can fly from Milan or Pisa, on/around those dates, to Marrakesh or Fez, for about £50–80 return.

Example: http://www.skyscanner.net/flights/mila/fez/120110/120131/airfares-from-milan-to-fez-sais-in-january-2012.html?flt=1

Use www.skyscanner.net to look at more options.

The boat, by the way, will probably be more expensive and will also take days.

From Croatia? Cheapest is probably taking a bus via Turkey. Depends where in Africa you want to go. Another way by land is via Spain and Gibraltar. Otherwise take a ferry.

You would need to travel during an off peak period even though it depends a lot on the airlie and the distance (country you are travelling to).