Apparently, you don't actually need to be a PR to apply, but it is looked upon favourably if you are
Actually, on the SLA website it says you must be a PR to submit the application form. Basically, a PR submits the form (Form A), pays the $520 application fee, and waits 30 days. If it's approved they then have 6 months to buy a landed property before the approval lapses.
This applies to leasehold as well as freehold, unless it's on Sentosa.