The best way to get here is to catch the Metro to Lesseps station and follow the signs, it is quite a trek and there are buses which run past the park entrance. Some of the tourist buses have a stop near the park, but you still have to get up the hill. And it is a hill. There are even escalators in the pavements
This route will take you to the main entrance at Carrer d'Olot, you pass through some amazing buildings and it is the first hint of what is to come.
There are a couple of free downloadable apps for iPhone and iPad that will give you a guided tour around the park, there is free wifi too if you want to interact.
Up until October 2013 the park was free to enter, however a charge has now been introduced for the 'Monumental Zone', in other words, where most, if not all, of the buildings are. The cost is €8 per ticket (€7 if bought in advance from the website) and 400 people per half hour are allowed entrance. I think it is a shame, but I can understand why it has been done, 1000s of people walking, running and climbing over the buildings is going to have an effect and maintenance cannot be cheap
More details of the park can be found here.