The most scenic route would be through Teguise, the former capital of Lanzarote, up through Los Valles (LZ 10) to some stunning views of the island and down into the beautiful province of Haria, the Valley of the Thousand Palms. From Haria, take the road to Mirador del Rio (LZ 202), where you pick up signs for Guinate (the Village) and Guinate Tropical Park & Penguin Paradise.
Alternatively, you can take the ring road around Arrecife to Tahiche (LZ 1) all the way to Arrietta, where you pick up the LZ 10 that takes you up a hill and to a round-about which if you take the first right will take you through the quaint village of Maguez and on to the road to Guinate.