Walk to "El Arcangel" Shopping Mall, and from there walk across Escultor Sebastian Cuevas street. Passing a plane (!) on your right, and then the football stadium, you will see a traffic circle and signs that divide the road towards Madrid, to the left and Malaga, Granada and Sevilla to the right.
You can just wait on the side of the road, right before traffic lights. If you are heading to Granada, hike a little bit further onto the freeway, as there is a very wide shoulder and traffic tends to move slowly.
Be careful because in Spain to hitchhier in motorways and its entrances is forbidden, so do not get too close to the motorway if you want to avoid problems.
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(Bus line 9, "Huelva" stop. Or just walk from the city centre.) Walk to "Puente de San Rafael" and cross it. When you reach a roundabout, turn to your right to Avenida de Cadiz, and continue following the right sidewalk. In 500m you will reach a Repsol petrol station, then a CEPSA, then eventually another 1km away is a BP https://goo.gl/maps/DcESP3n7SH12. This is the closest station to the highway and where one hitcher got picked up (after a 5 hour wait!) in 2016. Try to get a lift to the next petrol station in the motorway or to "La Carlota", a town 30km away from Córdoba.
Early in the morning there will be a lot of traffic going outside Cordoba (in 2016 this wasn't really the case), but it decreases as it is getting late. In the afternoon/evening, almost all traffic will be local. >> Seriously. I started at 9:00 which was apparently already too late in the day.
If you get desperate, walk about 1 km more down a bridge and you will reach an industrial estate (<not sure where this is). Try to find the entrance to the motorway, make a good banner and try from here. Consider to write "Proxima gasolinera" (next petrol station) at the back of your destination, to increase possibilities. Remember that in Spain, to hitchhike in motorways and it entrances is forbidden. Take your time to understand traffic flows, since the estate is chaotic. Considering all this, be strategic to choose a good place.
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Go to Plaza de Colon and find the line E bus stop. You have to go to the prison stop, and not all the E buses reach this place. From Monday to Friday the one at 2pm and the one at 7:45pm are OK, and at weekends you have up to six buses a day to there (have a look to the timetable). To ensure, ask the driver whether her/his bus reach the prison("¿Este autobus llega al centro penitenciario?"), and if not, ask for the next that do ("¿Cual es el proximo que llega alli?"). The bus will cost EUR 1.10. Use the time in the bus to make a good banner with your destination, you will use it in a while.
When you leave the bus, with the prison at your back, walk to your right to reach the motorway. Once you are there, cross the bridge over it, and in the round about at the other side, if you turn to your right, you will see two lanes in front of you, separated by a fence: The one at the right of the fence is the motorway exit (ignore it); the other one, at the left of the fence, is a service road. Walk across it for 1.5km to reach a petrol station, and do show your recently made banner, since all the traffic in this lane comes from the station you are going to, and if you are lucky you can save some time and energy.
If you have or make friends in Cordoba, ask them to take you to the petrol station near the prison. To leave Cordoba from "scratch" is difficult, and there are very few buses to reach the prison. And if you find the right people, they will be helpful with you.
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In the petrol station, spend one (perhaps two) hours to find a long ride, at least to Madrid if you go there. It is a very good place to hitchhike, and many cars and truck are going to the north of Spain. After this time, if you feel like that try to reach another petrol station, but do avoid any ride to Montoro. There is a bullshit petrol station there, in nowhere, and if somebody takes you there you will spend hours to leave.