Head to the main entrance of Parc Güell--also known as Park Güell--at Carrer d'Olot 7, Carretera del Carmel. You might do well to take a taxi there, because the closest Metro line, L3 to Lesseps station, and the closest buses don't get that close. The park is open daily from 10am to 6pm in the winter and 10am to 9pm in the summer. Admission is free. There are about two miles of pathways and trails here, so wear comfortable shoes and prepare yourself for lots of steep climbs. You also might want to avoid the park on holidays and weekend afternoons, when it can get crowded.
Observe the elaborate wrought iron gates and the houses to either side. The house to the left is said to represent the cottage of Hansel and Gretel, and the one to the right that of the evil witch that tormented them. The witch's cottage now houses an interpretive center with displays on the history and design of the park, as well as staffers who can help you find your way around. The center is open from October to March from 10am to 6pm, April to June from 10am to 7am and July to September from 10am to 9pm. The other cottage features gift and coffee shops.
Climb one of the staircases up the hill and past the sinous form of an enormous salamander, covered with mosaic tiles and with water spurting out of his mouth. You'll go up more stairs and pass more fountains before you reach the Sala Hipostila, a columned pavilion that Gaudi designed to be used as the market for the housing development. Over the eighty-six Doric columns is a ceiling of numerous coves, decorated with religious, mythological and astrological symbols. There's a large observation deck over the Sala and back behind that, a café. Also on this terrace level is the mosaic-covered Serpentine Bench, supposedly the longest bench in the world. It was designed by Gaudi colleague Josep Maria Jujol.
Go to the east and you'll see the Casa-Museo Gaudi on Carrer del Carmen. This was built to serve as the model home for the development, but Gaudi wound up living here himself from 1906 to 1926. It contains his furniture, personal items, artwork and architectural drawings and is open April to September from 10am to 8pm and October to March from 10am to 6pm. Admission is charged.
Proceed up to the northeastern end of the park to the Casa Trias. It's not open to the public, but the view nearby is spectacular. And if you head up the Turó de les Tres Creus at the southwestern part of the park, you'll see three stone crosses, as well as a panoramic view of Barcelona and the Mediterranean beyond.