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A swap is nothing more than a bunch of cashflows, which are to happen in the future. Usually the dates are fixed in advance, and the cashflows in one direction are also fixed, but the cashflows in the other direction won't be known until they are due. The two cashflows are usually netted off against each other, so the net payment could be in either direction.
Your question specifically refers to the contract, which usually is an umbrella contract so that multiple swaps can be carried out under it, each with its own confirmation note detailing the terms of the individual trade. These confirms are automatically incorporated into the contract.