Firstly it depends on where you're from ... at the moment I'll presume you're from the UK.
Technically you would need a visa if you were coming for the full season, even if it was just for a holiday, although if you leave every couple of weeks as a lot of people do maybe with a trip to the airport or something like that then you're technically not in the country for more than a couple of weeks at a time so don't need a visa. This is a grey area though. This would be classed as a "passive residency" and you would need to pay a bond to the government somewhere in the region of €30,000 which you would get back less administrative costs when you leave!
If you or your partner plan to work then you 100% need a work permit (green card) which needs to be sponsored by an employer, so you need to get a job first and then the work permit. In order to get a work permit you need a legalised police report, which is explained on our page about
working in Pas de la Casa. For instructor jobs there is only one school in Pas de la Casa, which is operated by the company who operate the mountain, called Grandvalira.
I hope this helps!