I didn't have a suitable container so I keep the beetles in a deep plastic box with mesh on top to stop them flying out . The info I downloaded said "when they start dying ....". Mine were showing no sign of dying off so every month I take all the beetles out (by hand) and tip everything into another container so the eggs can hatch. Don't throw any remains of veg you put in there away as the often lay their eggs on it! I have an old cat litter tray and some old washing up bowls. Then I put clean bran in the beetles box, replace the bits of eggcrate and give them some fresh greens - and repeat the process a month later. I got a bit lax about it and found some quite sizeable mealworms in amongst the beetles!
Having had loads of mealworms hatch out (in two containers), I eventually sieved those to get rid of the "frass". The poor things were living in about 2 " of frass and very little bran. I combined both of those so now have one container of mealworms of varying sizes, one container of a diminishing number of beetles, and one container which should be hatching mealworms as it was the last "beetle empty". (Note to self - go and check for signs of tiny mealworms).
It takes time for the eggs to hatch, a couple of weeks if I remember correctly. The way to check is to scoop some of the bran on to your hand and watch for a few minutes and you may see the bran move. The newly hatched mealworms are REALLY tiny, quite difficult to spot, but if the bran moves there's somethinhg there.
When the mealworms start to pupate you must remove the pupae form the box - mealworms are horribly cannabalistic. I just keep the pupae in a pot until the beetles hatch (they are cream and brown initially, changing to black as they harden off) and then move them into a container as described at the top of this post. I'm hoping that the existing beetles will have died off by the time the new ones hatch, as they are dying off quite quickly at the moment.
When I started I kept quite a lot of the original purchased mealworms in boxes in the fridge to feed to the hens as it takes a couple of months before you get your own. Just make sure they have some vegeatble matter - leaves or a sliced carrot to give them moisture. It's very important for the beetles - I read somewhere that if you put the newly hatched beetles on a slice of dampened bread they lay sooner but I haven't tried it.