DVD links are not part of the general spec of DVD-Video. They are a popular extension though. Popular in commercial DVD-Video offerings anyway. Made this way through utilizing a protected trademark facility from InterActual that featured in many early generation PC based DVD players (often using dedicated hardware decoders with video output and VGA (black-keyed) overlay (such as SigmaDesigns Hollywood+/Creative Labs DXR series). The capability extends into many modern day software players and indeed some internet enabled set top boxes.
It is a licensed capability so as for set top boxes generally (with IP/ethernet interfaces) this is still a feature that is about as rare as native SACD or DVD-Audio capability.
As for authoring it, well- Sonic Solutions adopted the technology with such vigor that they bought InterActual in 2004.
autorun.inf (Windows) and autostart (OSX) have various options to start either alongside or instead of your natural DVD player software (assuming PC playback rather than an internet enabled appliance like an XBOX 360 or PS3 etc).
Later versions of Windows allow both executables and scripts to be immediately referenced by the autorun.inf. Earlier versions aren't so flexible making at least a 'loader' executable necessary. Making this type of stuff work universally isn't unlike the earlier days of making a website work with both IE and Netscape. I suppose it is somewhat safe to assume that your audience will be using Windows 2000 or newer?
http://www.ashzfall.com/products/autorun/browsercall.html
There are a number of free and commercial offerings that make use of the tendency to initialize on these components prior to the computer subsystem noticing that your disc also contains a DVD-Video structure. Google for 'autorun.inf multimedia dvd-video' ....
Making the web link appear at the end of play of the DVD-Video (especially if the movie has a menu or can be paused or skipped) would be a challenge to code for without the interactual hooks. Scenarist etc isn't cheap and interactual is an add-on afaik.