Well, the application process (and the requirements) are different depending on which Comunidad Autónoma (Autonomous Communities, something like "states") you want to study. They are more or less the same, but some things may differ.
You should know whether you want to study in Madrid, in Barcelona, in Salamanca, in Navarra, in Valencia, etc. There are plenty of unis.
Once you know, you have to homologate your grades and qualifications (info
here and
here). You may have to do the "Selectividad" for foreigners (if you're doing A-levels perhaps you could avoid doing it, but I can't assure you, you better contact the
Spanish Ministry of Education), you may find info about it
here,
here and
here.
Here you may find info about straightaway homologation between British and Spanish grades, no need for Selectividad. Anyway, if you're doing your A-levels with CIE, this might be different.
This year the Selectividad is changing (both for Spaniards and foreigners), but the mark you will need will be quite high (probably about 90% or 95% overall). I imagine you are doing A-levels. Look at the chart where UCAS points are compared to those of Bachillerato + Selectividad (last link, . 380 points (A*AA) would give you a 74% overall in the Spanish system (7.4). In order to have a 100% (10) you would need AAAAA (or 600 UCAS points).
After that, you need to be fluent in Spanish (have the DELE or pass the Spanish language in the Selectividad, I think). Besides, if you're to study in Catalonia, the Balearic Islands, the Valencian Community; the Basque Country; or Galicia; you will also need to be fluent in Catalan (Valencian and Majorcan are more or less the same); Basque or Galician (similar to Spanish and Portuguese).
The application process begins in May/June for entry in September the same year. As far as I know no PS is required, nor interviews, and you will know if you're admitted about the second week of July.
You have to apply through the Autonomous Government, at least in the case of Catalonia, (here) through the
Generalitat de Catalunya (info also
here). I don't know about limits or details of the application, you may like to check up the website.
Once you have been given a place in the uni (no such things are offers exist here, you apply to unis and if there are 200 places and 300 applications, the first 200 are given a place, and then they decide whether they want the place or not, in case a person does not want it, the 201st is given a place, etc.), I guess you need a student visa (in case you're not European). And arrange accomodation and stuff.
By the way, don't expect the government-employed Spaniards help you with anything, rather the other way around. And, I don't know if non-Europeans pay home fees here in Spain as well, but I may assure you that, at least in Madrid or Barcelona, the cost of living is higher than in the UK (perhaps excluding London, perhaps not even London would be excluded).
Degrees (bachelors) are being put into service this year, so the system is not very good implanted as of yet. Which means that the very same degree with the very same qualification to any European counterparts will involve an extra year of study (in the UK 3 years, in Spain 4; in the UK 4 years, in Spain 5; and so on...).
If I were you, I would not come. The social situation is very bad. The unemployment is about 20%, the salaries are low compared to prices, and it is really hard to find such a thing as a part-time job to help you funding your studies.
Whatever you need, you ask me.
Good luck.