Visa-free stays involving paid activity in the Schengen Area - how do they work?

Wikipedia mentions that citizens of certain Annex II countries are eligible to work in some parts of the Schengen area during their short-term stay. However several aspects are not entirely clear:

Does the right to work get activated automatically upon arrival?
Are immigration officials aware of this law, so one can safely announce their intention to work upon arrival?
What documentation can be showed to would-be employers to prove that this rule exists on the books?
Are there any websites specifically catering to Annex II individuals seeking short-term work in the Schengen area?

Note that since the default 90 out of 180 rule still applies to such trips, this question is on-topic for Travel.SE.

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How long can you stay in the Schengen Area without a visa?

2. How long can I stay without a visa in the Schengen area? You can stay 90 days in any 180-day period within the Schengen area.

How does the Schengen Area work?

The Schengen zone includes the 26 countries that have signed the Schengen agreement, which allows citizens of member countries to travel within the zone freely, without passing through passport and border control. Each member country of the Schengen zone can issue Schengen visas.

What happens if you overstay in the Schengen zone?

You could receive a fine, immediate deportation or even get banned from entering the Schengen Area for a period. It is also important to remember that the 90/180 day rule also applies to countries with a visa waiver agreement with the Schengen Area.

How does the 90 day Schengen rule work?

So, when you apply for a Schengen Visa, no matter the Schengen Member State, your visa will be valid for 90 days per 180 days. This means that you may only spend 90 days within the Schengen Area, no more than that. If you overstay, you risk deportation or getting yourself banned from the Schengen Zone.

What is the Schengen Area and how does visa free travel work?

Sources: Stack Exchange - This article follows the attribution requirements of Stack Exchange and is licensed under CC BY-SA 3.0.

Images: Tatiana Syrikova, Vanessa Garcia, Allan Mas, SHVETS production