Best way reach Montjuic is by cable car
Montjuic is fairly large in area, so the best way to get to Montjuic depends on which part of Montjuic you want to go. Assuming it is the Montjuic castle, the best way to reach is by cable car (Teleférico de Montjuïc).
The Montjuic cable car is a gondola lift that runs from its boarding point near Montjuic Park (Parc de Montjuïc Station) all the way up the mountain to Montjuïc Castle terminal. You get 10% discount if you book tickets in advance online.
You have various options to reach the boarding point of Montjuïc cable car.
a)Barcelona Tourist Bus
As a first time tourist, if you are utilizing the Hop On Hop Off service, the Red route drops you to the boarding point. What's more, the coupon booklet will also get you €2 discount on the cable car ride.
There is a funicular train that operates from Paral.lel Metro station to the boarding point of the cable car. If you come by metro to Paral.lel Metro station, funicular is counted as part of the same trip .The Paral.lel metro station is on metro lines L2 (from City Centre) and L3 (from Plaza Espana).
c)Port cable car
If you are coming from Barcelonata beach, take the Aeri del Port' ("Port Cable Car") and then interchange to Teleferico de Montjuïc. The ride on the Port Cable Car is recommended as the views are varied and excellent.
By bus to Montjuïc Castle
You can board Bus 150 - Pl. Espanya to Castell de Montjuïc. The bus zig-zags on the uphilll road and will deposit you right next to Montjuïc Castle.
If you are looking to get to other attractions of Montjuïc, then take the funicular from Parel.lel metro. Visit the Miro Fondation, then stroll down to MNAC. From MNAC, you can use the escalators to the Magic Fountain.
Best approach to Montjuic is from Pl. Espanya
If you want a nice scenic route passing many attractions on the way, first get to the metro Pl. Espanya.
From Espanya you will take escalators up to MNAC, after you pass Font Magica, all the way up the hill. The escalators will reach the road near there Olympic Stadium, Miro Foundation and Poble Espanyol.
The ride up on the escalator has stunning views of the city as you go up.
This option is a much nicer access than taking the funicular from Paral.lel metro stop, which is on a different side of Montjuic hill, and does not offer much scenic beauty.
If you are more conveniently located near Paral.lel, then take the funicular up to the castle and use the escalators to come down after you're done. This way you can time it so that you are down near Pl. Espanya in time for the Font Magica show.