regular calls to a script
 

I have gotten to a point in a project where I need the server to run a script (ideally in php, because that's what I know) at regular intervals (like every hour, or less if possible).

How do I go about that? Is it just as simple as, either the hosting company offers that service or it doesn't? Edit: And if it is just the hosting company, can anyone suggest a good hosting company that's either free or cheap, and offers that?

Sounds like a cron job. Whether you have the permissions for that is problematic.

if the platform is windows, you can look into a scheduled task, otherwise a cronjob would suffice.

I read a bit about cron, and it seems to be what I'm looking for. But I can't find anything about it on the support pages of my current hosting company.

I would contact them about it. See if you have that type of permissions on your host server.