An ATA Carnet is a multi-part document which is used to confirm an inventory of items which are taken out of the EU and returned within a pre-determined time. This is to prove that they have not been exported, or indeed imported when you return. Failure to complete all sections properly at any point when entering or leaving the EU will result in claims for duty/VAT, which obviously can be quite large when considering the value of most broadcast equipment.
Before leaving, you have to submit an inventory of the equipment which must include product type and serial number, country of origin and value. This information is printed on the back of the Carnet's green front cover together with item numbers.
On leaving the EU, the front cover must be signed and dated by the shipping agent's representative, i.e. you! Then at each EU entry or exit point you need to sign and date the appropriate multi-part form and fill in the location, means of transport (usually flight number) and item numbers included (hopefully all of the ones on the green list). Customs will stamp that form and retain it and fill out one of the exportation or reimportation vouchers which stay within the pack. Whatever is left must be sent back to the shipping agent when you return. It is strongly recommended that you return it by special delivery.
The colours of the various parts of the documents indicate their usage. The front cover is green, documents used at EU borders are yellow and documents used at non-EU borders are white.
At any point Customs may inspect the goods. This can vary from show this or that item (common) to a complete opening of every box and detailed check aginst the carnet (rare).
Hints & Tips
When submitting your inventory you don't need to list things like cables individually - just write something like "cables and adapters" and include this as one item. Try and avoid words like "various" or "assorted" as these can look suspicious.
Tools and stationery goods should just be entered as one item - the favoured term being "tools of the trade".
Some countries are not keen on words like "radio" or "wireless". Even if you have the correct licences (you do don't you?) it is something else for the customs officals to look through and check.
In the UK ATA Carnets are issued by The London Chamber of Commerce, they have an FAQ on ATA Carnets.