You may know already, in which case you are excused from reading this - and welcome to add comments, and correct me if I'm wrong.
A hung parliament means that there is no individual party that has an overall majority of the seats. With 650 seats in the House of Commons, a single party needs to secure 326 of them to have a majority. Otherwise, all of the other parties ganging up together have the capability of defeating the government when it attempts to pass any law, potentially incapacitating government. Most significantly, this is relevant in the case of a "No confidence vote" - a vote which declares that the rest of the Commons have no confidence in the government. I believe that if the government loses a no-confidence vote, then the prime minister has to resign.
The ball is, initially, in the court of the Prime Minister. Gordon Brown continues to be the Prime Minister, in constitutional terms, until he no longer has the confidence of parliament (ie. he loses a No Confidence vote). He could do various things. He could attempt to form a minority government, although he is the leader of only the second largest party (at the time of writing, Labour have less than 249 seats, whilst the Conservatives have 291 and the Liberals have 50, and about 35 more to be declared). However, this almost certainly wouldn't work - the Conservatives could very reasonably call for a No Confidence vote in these circumstances - Labour had fewer voters and fewer seats, and therefore don't really have a mandate to continue to be the party of government.
Brown's next obvious option would be to seek a coalition with the Liberals. This may still not give the government an overall majority (315 seats, once all the votes are counted?)! By drawing in the other small parties, it may be possible to organise an alliance which technically commands an overall majority. However, alliances of lots of parties tend to be unstable, and it would be unlikely that such a government would last very long.
Incidentally, this is why the situation is regarded as so uncertain at the moment. A lot depends upon exact numbers of MPs, and people are vary cagy about revealing options when they don't know exactly what they might be.
Another option is for Brown to resign. In some ways, this would be the "honourable" thing to do, since Labour "lost" to the Conservatives. There are other potential benefits for the Labour party. The Conservatives also won't have an overall majority, and they are likely to find it harder to form a coalition government with other parties than Labour. The effect of this is that it may also lead to a government that doesn't last long, but the failure of the government would be a Conservative failure.
Probably the best option, given the financial crisis that is being faced, would be for the three parties to recognise that none of them commanded the enthusiasm of the voters, and that they ought to work together to deal with the economic crisis faced by the country. Either Brown or Cameron could organise this - and form a government made up of all three parties. Neither wants to, of course - the party manifestos would go out of the window, and the government would have to work together for what it decided (together) would be the good of the country. But if any conclusion can be drawn about the outcome of the elections, it is that no party has been given a mandate by the electorate to do the things they want to. If the parties take seriously their stated views about "listening to the electorate", this deserves serious consideration.