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The fastest way is to start at Taganga which is just North-East of Santa Marta and take a boat that drops you at the docks on Cabo beach. The trip takes just under one hour and officials are waiting there to collect the park fee and check your bags for forbidden items. Once past that, you are in and already on a beautiful beach. It takes 20-30 mins to walk to each beach further west.
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In Rodadero (tourist town 1km from Santa Marta), there are tours that go to Tayrona park, and cost around 10~15USD per person (YMVV, if you bargain you could get better prices).