The answer by Craig Gidney is quite adequate for the question, but I want to address the word "collapse" in the title, since search engines will be homing in on it. From webster.com
1: to fall or shrink together abruptly and completely : fall into a jumbled or flattened mass through the force of external pressure <a blood vessel that collapsed>
2: to break down completely : disintegrate <his case had collapsed in a mass of legal wreckage — Erle Stanley Gardner>
3: to cave or fall in or give way <the bridge collapsed>
4: to suddenly lose force, significance, effectiveness, or worth <fears that the currency may collapse>
5: to break down in vital energy, stamina, or self-control through exhaustion or disease; especially : to fall helpless or unconscious
6: to fold down into a more compact shape <a chair that collapses> Definition of the word "collapse", Webster's dictionary
Note how the word describes a physics situation.
A wave function is a mathematical formula with complex numbers, posited for all particles in the quantum mechanical framework, from which the classical dimensions we live in emerge. It is a mathematical expression of a very successful model which, when squared with its complex conjugate gives a probability density distribution for observing with real numbers the problem at hand. In the case of the double slit experiment, the probability of finding the photon at the specific (x,y) of the screen.
The wavefunction exists in our copy books and our computers as a mathematical formula valid continuously. It is an unfortunate label that the word "collapse" has been attached to any property of the wavefunction. The wave function does not break down in any of the senses of the definition of the world collapse. It is always there, in our copy books and computers. A single measurement picks up an instance, and accumulation of measurements gives the probability distribution that the wavefunction so successfully models.
Example:
Take this paper which gives Probability of delivery within x days of a given date, the date given by the doctor from the data the mother gave.
The birth of a baby will be an instance of this plot, which accumulated with more instances should verify the distribution shown. Is anything in any logical way collapsing, according to the definitions of Webster?
I hope this makes clear that collapse is a wrong word to use for a mathematical distribution, attributing reality values. It is at worst an anthropomorphic word, giving human attributes to a mathematical formula, at best a misguided identification of the complex mathematical formula to the real formula of a collapsing balloon. The wave function is not a balloon either.
Great question! I suspect the reason you can't find videos (although I haven't looked for them myself) is because most of the videos of interference will be videos of photon interference, since that is the easiest kind of interference experiment to do. However, the only kind of measurements we can perform on photons in this experimental context are what we call "destructive" measurements: for example, you could just block off one of the two slits, and then for any of the photons that get through you will know which slit they went through... but you will be destroying the other half of the photons.
This is therefore not as compelling an illustration of the collapse of interference patterns as an experiment in which you can measure which slit the particles go through while still allowing them to pass through the slits. For this, you need to use some other kind of particles, such as electrons. This has been done, and the interference pattern indeed collapses when you measure which slit each electron passes through, but I still don't know if there is a video...
Best Answer
The other answers here, while technically correct, might not be presented at a level appropriate to your apparent background.
When the electron interacts with any other system in such a way that the other system's behavior depends on the electron's (e.g., it records one thing if the electron went left and another if it went right), then the electron no longer has a wave function of its own: the electron+"detector" system has a joint state. The two are entangled.
The electron doesn't have to "know" anything. The simple physical interaction results in a state vector which, by the laws of quantum mechanics, will preclude interference by any of the subsystems of this larger system. That said, the joint state can itself show a kind of "interference effect" (though not the kind you normally think of in the two-slit experiment).
If this entanglement is well-controlled (as in a lab), then (a) showing this "joint interference" might be practical, and (b) undoing the entanglement is also possible, thus restoring the electron's sole superposition. This is how we know that it hasn't "collapsed."
But if the entanglement is caused by stray photons, air molecules, etc., then any hope of controlling them becomes almost immediately dashed, and we can no longer exhibit interference in practice. From here on out, the system will appear to behave classically, with the different branches evolving independently. This fact is called decoherence. The superposition still hasn't "collapsed," but we no longer have the ability to show or exploit the superposition.
You may notice that this still leaves open a crucial question: when do the many branches become one? This is called the measurement problem, and physicists don't agree on the answer even today.