Lanzarote

 is an island, part of Canary Islands, Spain. Hitching in / out, you could try Hitchhiking a boat.

Out of the airport
Directly asking people that have just dropped of someone in front of Departures gate seems to work well.

Out of Arrecife - Direction North (Tahiche, Haria)
End of Calle Leon y Castillo (top of the hill) - next to a big Eurospar with a big parking lot in front of it, is a bus stop. Works best with a sign! (And if you can't catch a ride, you can still take the #7 or #9 bus.)

Out of Arrecife - Direction South (Airport, Puerto del Carmen, Playa Blanca)
Find the bus stop "Intercambiador" on the seafront, at the other end of the main Arrecife beach (beginning being the high-rise glass hotel). Directly next to it is the big Island government building (Cabildo). Follow the road for about 200m (roundabout and underpass under motorway) and you'll be at a roundabout that takes you up to the motorway in the desired direction. Easy to stop and very good success rate.

Accommodation and Sleep
Wild camping is prohibited in some beaches, but it's generally regarded to be fine if you stay over at one place, then move the next day.

Or contact the CHT nomadbase / hackbase.

Other useful info

 * Hitching is generally good.
 * Distances are short and it's almost always possible to pull on the side of road - no real motorways - so try walking and hitching!
 * Signs will help you a lot (with name of a specific village)
 * so will basic Spanish
 * Hitching at night worked too - standing on the sides of the road with a flashlight on the sign.