The idea of compulsory voting is a non-starter. At present we cannot stop young people murdering each other. Quite how we intend to compel two thirds of the population to spend 20 minutes away from the telly every five years doing something they have no interest in needs some explanation. There are less than 1000 murders a year - so me thinks that you exaggerate too much.
Very simply, a law that makes it compulsory to vote, on punishment of fine (in a similar way to council tax). It is not difficult, and although there will be people who protest and do not vote, the majority of people (in my opinion) will happily go down to their voting booths. I would also do this for local elections, so it would be an annual event. Maybe a bank holiday should be declared on that day as well so that there can be no excuse. Maybe (and I do use the word maybe), technology can be used so that people can vote on line or by phone / text. This would of course have to be done correctly.
Rumour has it that more people voted in a big brother competition that voted in a general election. Young people have to take on certain responsibilities - and this is a good starting point.