To obtain surf the player must have $20,000. Before getting surf, it would be very useful to have a water Pokemon in your party as it lets you exit the safari zone much quicker, now proceed to the northern area of Fuchsia City, where they will enter the building at the very top of the map.
Next, speak to the NPC to buy a 24 Hour Safari Zone Ticket for $20,000. The ticket activates as soon as you agree to buy the ticket so make use of your time spent there.
Follow the map provided to reach the West Zone.
Once you have reached the west zone, proceed to the house on the top left hand side, once inside speak to Darren and he will give you Surf. Exit the building and teach surf to your water pokemon if you did bring one, surf accross the pond and you can exit the safari zone.