Can I record or download a film that has been broadcast on television or is available online?

Both recording and downloading are regarded as reproduction. This requires the creator's permission and you have to pay them a fee.

There are a number of exceptions, depending on the purpose of your copy.

You can copy an entire work for your own personal use without permission (Articles 16b and 16c of the Dutch Copyright Act) as long as this copy is made from a legal source. You are already paying an indirect fee for this, the so-called home copying charge. It is important that a copy intended for your own study or personal use is not disclosed to the public, for example by showing it in an educational setting. As soon as this personal copy is disclosed, it leaves the private sphere and 'personal use' no longer applies. At that time, the creator's permission for showing it must therefore be requested and a fee will have to be paid. This therefore also applies to a video that is shot at a student association.

If you want to record or download a video film to show it in an educational setting, you may do so based on exceptions 2 and 3 for education. Recording or downloading from illegal sources is also not permitted.
In short, exception 2 allows you to copy (and show) short works in their entirety, but only part of longer (audiovisual) pieces. You also have to pay fair compensation the rightsholder for this.
The right to quote (exception 3) makes it possible to copy and disclose an extract of a video or a short video in its entirety free of charge in the context of an educational or scientific thesis.
As mentioned in the exceptions, many resources of the Dutch public broadcasting corporation may now be used in an educational setting, provided that a 'Beeld & Geluid op School' licence has been obtained. There are also some videos on the Internet that the creators have given their express permission to reuse either commercially or otherwise. They may do this with a Creative Commons licence, for example. In that case you can copy and show these films free of charge. A credit to the author (attribution) is usually required. You can also stream the film online, so you don't need to create a copy before watching it.

More information

Copyright fundamentals
Creative Commons
Beeld & Geluid op School