WnT has it mostly right, but the 'natural born' requirement is pretty much an American thing. Neither Canada nor the UK requires you be 'natural born,' though it surely helps in practice.
Another niggle is that you needn't necessarily hold the majority of seats in the lower house of Parliament. (Yes, there are usually two--the lower, the House of Commons, holds the primary power while the second is supposed to supply 'sober second thought.' In Canada the upper chamber is the Senate, in the UK it's the House of Lords.)
Because parliamentary systems often are not confined to two parties, as is the case in the US, it is possible to have "minority government." Usually this means that the party holding the largest number of seats governs, although they do not hold enough seats to form a Parliamentary majority. (For example, if there were 450 seats in the House of Commons, and Party A had 200, while Party B had 150 and Party C, 100, then usually Party A would form the government.)
When this happens, the Government needs to enlist the support of at least one opposition party to pass legislation. A variation on this theme is the coalition government, where two (or more) parties agree to share power. (In the example above, parties B and C might be able to form a government by coalition, forcing Party A out of power.) An real example of a coalition is the current government of the UK, which is formed by a coalition between the Conservatives and the Liberal Democrats.