My personal favourite alternative is STV,but in the referendum on May the 5th we only get the choice of first past the post (FPTP) or alternative vote (AV).
Very simply, under AV, instead of putting an 'X' next to your preferred (or, more likely, least disliked) candidate, you rank the candidates in order of preference: 1st, 2nd, 3rd, etc. You can rank as many or as few preferences as you wish. Here's an example of an AV ballot paper from the Labour leadership election:
When it comes to the counting of the votes a system is used to ensure that the winner is the one who is supported by over half the voters. This works by dividing the counting into rounds. In the first round, if anyone has got over half the first preferences then they win automatically. But if no one has a true majority in the first round then the candidate with the least number of first preferences is eliminated (let's call her the Orange candidate). But what happens to the votes of the people who voted for Orange now that she's been eliminated? Well, their votes get redistributed. So if their second preference was for Yellow then their vote is transferred to the Yellow candidate. If, after the votes have been redistributed, no candidate has won a majority of 50% of the votes then the candidate with the next least number of votes is eliminated and their votes are redistributed using the same method as above. If, for example, it's Yellow who is eliminated in the the second round, then the Orange voters who'd put Yellow as their second preference have their vote redistributed according to their third preference.
So, if an Orange voter had voted Orange , Yellow  and Red , their vote would go to the Red candidate after Orange and Yellow is eliminated. This means that everyone gets one vote in each round.
The process is repeated until one candidate gets over 50% of the votes and is declared the winner. This means that the winning candidate has to be one that the majority of voters are happy with. It's like asking a friend to go down to the shop to get you a coke. You might say to them "if they don't have coke then I'll have a pepsi instead but please don't get me Dr Pepper because I hate that stuff". AV is the same principle applied to our electoral system. The candidate who becomes MP is one who most people can be happy with, even if some of them might have preferred a different MP in an ideal world. Above all, what it does is make sure that no one can be elected on 20% of the vote even though 80% of voters didn't want them.
So that's why, on May the 5th, I'll be voting Yes to AV. FPTP is broken and we need an improvement. AV might not be the best system in the world, but it is far better than what we've got. Please say 'Yes' to fairer votes.