Nothing special - I put it in a 500ml plastic food tub with a snap-fit lid (e.g. tub for creamed honey), there's enough air inside so it won't suffocate in a relatively short period of time. The specimen is actually resting on the lid of this tub - a nice flat white background for pictures.

It might be tempting to use a glass jar, but I think that would be a mistake. Glass is a decent thermal insulator and would take some time to cool from room to refrigerator temperature, which could make timing inconsistent. If you wanted to use a glass jar you could keep it in the fridge, and transfer your specimen to the pre-cooled jar - but that's a bit of a hassle. A plastic tub has low thermal mass and plastic is a poor thermal insulator, so the cooling effect is felt almost immediately. If you could find a clear plastic tub, that might be the best of both worlds.

Then I put it in the refrigerator (not the freezer portion) and checked its activity (cracked one edge of the lid up and peeked) every 10 minutes until it seemed sluggish enough to stay put for some photography. This specimen was good to go after 20 minutes.

Variables I suspect would have an effect on the necessary chilling time:

- specimen size: heavier (more massive) ones, with the same shape, will take longer to chill (square-cube law)

- specimen aspect ratio: skinny/slender ones (like walkingsticks) will chill more quickly than round/globular ones (like ladybugs). This is due to their higher surface area to volume ratio. Specimens with veinous wings will probably chill more quickly, as the wings act like radiators (assuming circulation to them does not shut down when temperature drops)

- specimen "insulation": insects such as hairy, cool-weather moths will be more resistant to chilling, all other things being equal

- original specimen temperature: all cold-blooded creatures have an optimum "operating temperature" at which they are most active. The idea of chilling is to lower their body temperature out of this optimum range. If the specimen is something like an early spring/late fall moth, whose normal operating temperature may be only a few degrees C above freezing, you might actually have to put it briefly in the freezer (below zero C) to chill it into sluggishness. On the other hand, an insect that hatches only on hot summer days will probably become sluggish very quickly even at regular refrigerator temperatures.

- temperature of refrigerator or freezer: this doesn't actually vary that much. I'd avoid the freezer unless trying to chill cold-weather insects.

Most (but not all) insects have evolved to be able to tolerate cool temperatures for a period of time with no permanent effect. As long as you don't overdo it (i.e. go too far below their "optimum" temperature for too long a time period) they should recover fine.