Procedures vary, depending on the rules of the country. In the US, many (most?) non-controlled airfields are in Class E airspace and radar separation is provided from other IFR traffic until landed or cancelling IFR. Once cleared for the approach you will also be cleared to change to the aerodrome's frequency, with a reminder to cancel IFR on the controllers freq. or via phone after landing. Until IFR is cancelled the controller will keep controlled traffic out of the way even though you may no longer be on ATC's frequency.
Meanwhile, you're responsible to communicate on the aerodrome frequency and arrange separation with non-controlled traffic operating at the field. It's much, much easier to do during really crappy weather ie non VMC to below circuit height, than when the weather is VMC at or above the normal circuit altitude. Not too many other aircraft to worry about when the weather is really dismal, and ATC will prevent other IFR aircraft from commencing an approach until you land, cancel IFR or are back being controlled again.
In Australia the vast majority of aerodromes are OCTA. Instead of a controller providing separation, a flight information service for known traffic is provided. You still have to coordinate your own separation from the traffic, including other IFR aircraft who also want to do the approach, and give broadcasts on the aerodrome's frequency to inform traffic that isn't involved with ATS/FS. Usually the first there gets to do the approach first while the others adjust speed & track to avoid a conflict, or everyone stacks in the hold to wait their turn. Lots of broadcasts of intentions & altitudes being left so others can know when they can step down etc.
Not quite a complete lack of FIS as your question asked but somewhat similar. Absent ATS/FIS then give lots of broadcasts of position, altitude & intention, and talk to the other planes that might conflict
Last edited by Tinstaafl; 25th Oct 2012 at 17:25.