There are as many recipes for this as there are Spaniards - but this is my family's (from Alicante) and completely authentic.

First trick is getting the right potatoes. In Spain we get those with red skins (no idea what they're called) - in the UK I tend to use Desiree potatoes or King Edwards.
New potatoes won't do, nor will any of the 'salad' potatoes which are too waxy.
You can use more 'floury' potatoes meant for roasting or frying, but the best for a tortilla are just a little firmer.

Now the main trick is to get the potatoes right. Peel them first and then hack away around the surface so you are making extremely squashed 'pyramids' or angular 'cones' - the aim is to get as much surface area as possible. Careful not to make them too thick - you're aiming for 'pyramids' no more than about 1/3 inch high with a diameter well under an inch. Just move the potato around in your hands as you hack away at the surface.

I'm assuming you'll be using a 9 inch non-stick frying pan. Cut enough potatoes to fill the pan two thirds to the brim (usually 4 to 5 medium/large potatoes should do this.)

Also cut into pieces a large onion - you're aiming for 1/2 inch squarish pieces.

You have two options available now

- fry the potatoes in a deep fat fryer until golden (doesn't really matter which oil you use - the olive oil taste will come later)

- or cover the frying pan with at least 1/3 inch of olive oil, bring up to heat (medium/high) and start cooking the potatoes stirring at least once a minute. When the potatoes just start to soften (and well before they brown) add the onions and continue to stir - hopefully they'll start to brown together.

If you've pre-fried the potato pieces, keep them warm and fry the onion in the 9 inch pan until soft and browned - put in enough olive oil to generously cover the base. Once the onions are done, add the potatoes and stir together, mixing the two and bringing the potato pieces back up to temperature.

Which brings us to the egg part. Beat at least 4 large egss (you'll need at least 5 medium ones) add another one if you aren't sure. Once the eggs are beaten together and look deliciously creamy and slightly frothy, add one lightly heaped teaspoon of finely ground sea salt (you can use any kind - different kinds of salt have different levels of 'saltiness' there's an art in getting the right amount - too little and the omelette will taste bland, too much and your tortilla will be way too salty) and beat through the egg - the egg should look a lot less appetising now!

Turn down the heat a little and pour the egg over the potatoes and onion in the pan and violently turn the handle of the pan in several clockwise (or counter-clockwise) motions.
(Right at the very start you can quickly stir the egg and potato mix together with a spatula - but only in the first ten seconds or so)
Continue jerking the pan round occasionally whilst it's cooking - this helps to prevent it sticking.
(This would be the time to add a little more egg if you think you've miss-judged the amount)
When you think the omelette is done on one side, lift one side gently with a spatula to see if it has lightly browned underneath.

Now for the tricky part. Hopefully you have a dinner plate or pan lid that fits closely inside the pan. To begin with, you might like to do this over a sink (if you're very frightened of these things, wear some rubber gloves and wrap a tea-towel over your wrist). Drop the plate over the omelette, put one hand firmly over the plate, your other hand should be gripping the handle and in one quick, deft motion turn the omelette over onto the plate.

Check to make sure you haven't got anything sticking to the pan (if you have - just scrape it off and addd a little more oil if necessary) and slide the omelette back into the pan from the plate. Continue to cook, again, jerking the pan around occasionally so that it cooks evenly.

If you find at this time that one of the sides hasn't browned as well as you wanted it to, just repeat the flicking around process and cook that side some more.

Once done, turn onto a plate in the same way, or just slide it off the pan.

If the tortilla has been made without onions, it's best served hot. With onions I like it warm, perhaps just a little above room temperature. It will keep well for the next day, but bring it up to room temperature as they are not that nice 'cold'.

You may like to dust the top with a little smoked pimenton/paprika (although I rarely do this).

Sorry this got so long winded - it's one of those things that's easier to show than it is to explain. Keep a note of how much salt, eggs, potatoes you used... don't be surprised if it takes about 3 attempts before you're entirely happy with the result. It's worth persevering with though - it's a fantastic dish to have in your repertoire. The whole process will take at least an hour - no matter how much you try and speed it up. We made loads of them for my wedding reception... alas, there just aren't any acceptable shortcuts (except for deep-frying the potatoes).