BBC Political Editor, Nick Robinson has this helpful summary.

No party has enough seats to win votes in parliament without the support of members of other parties.

The Conservatives are the largest party with a total of 306 seats in the Commons – which would go up to 307 — if they win the delayed election in Thirsk and Molton – until now, at least, a safe Conservative seat.

If they tried to govern alone they would, in theory, face a combined opposition of 343 MPs.

In reality it’s somewhat different. Sinn Fein won 5 seats – and they don’t take their seats in the House of Commons – so the opposition benches reduce to 338.

A Con/Lib Dem coalition would give them a total of 364 – enough to govern comfortably.

A looser arrangement in which the Lib Dems agreed not to vote against a Tory Budget or the Queen’s Speech would mean 306 or 307 Tories facing a depleted opposition of 281 (that’s 338 – 57 Lib Dems)

If a Lib Dem/Conservative deal fails, Gordon Brown will try to form a government.

If Labour and the Lib Dems joined forces – the extra 57 votes are not enough to make them the biggest force even with the support of the Northern Irish SDLP (who sat on the government benches in the last parliament) and the one new Alliance MP who is allied to the Lib Dems. Together that’s 319 votes.

With the support of the nationalists from Scotland and Wales they would reach 330.

If the DUP joined too and the independent unionist and the new Green MP this alliance would have 338 votes in the Commons.