If you look at a flight plan on FlightAware, the last code will be a STAR. Take a flight into JFK, for example, that uses LENDY6: the last waypoint of LENDY6 is the LGA VOR/DME at FL190. If the plane then lands on 04R, how does it get routed to final? Are there any documents that show this routing?
Look more carefully; says it right at the bottom. At the STAR's termination waypoint, LGA, expect radar vectors to final.
If you had comm failure, and couldn't talk to ATC, you would fly the STAR in your clearance and if it is an open STAR like that, at the termination waypoint you would find your own way to the ILS/LOC and shoot the approach, taking the most logical path to get there and avoiding any unusual maneuvers or turns.
A lot of the procedures you see in SIDs and STARs are not followed exactly as depicted when ATC is giving instructions (the controller may put you on vectors long before you reach the termination waypoint for example), but are there in case of a communications failure, to ensure that an arriving or departing aircraft has obstacle clearance and so that ATC can predict with reasonable certainty where you are going to go as you arrive with no way to talk to them.
As @JohnK wrote, it will be radar vectors. That means the air traffic controllers will be giving heading, altitude, and speed instructions to the aircraft.
The basic reason is spacing and merging. You have aircraft that are also arriving into JFK from other directions on other STAR(s) and often going to the same runway or parallel runway pair. So each plane will be vectored a bit differently, so by the time they line up to the runway the correct spacing (distance) will be achieved.
To help you visualize it, here's a snippet of some of the traffic arriving into JFK at the moment, note the two planes coming over LaGuardia merging with the rest, while staying above and clear from the approach path to LaGuardia.
Newer ATC systems have started employing time-based (as opposed to distance) spacing. It's one of the steps towards 4D traffic management, which beyond 2030 should make this process a bit more automated and rely on data comms (vs. voice) with the aircraft being able to communicate their performance and trajectory (see: ICAO B3-TBO).