This is how you breed crickets
This is how I breed crickets. There's 1 thing to consider first off: if you cannot keep all life stages above 85 F this is not worth your time.
I keep crickets of all stages in large rubbermaid bins with a screen lid. I only feed chicken layer mash and have no trouble whatsoever. Water is provided in a 4.5" delicup lid filled with water crystals. Water crystals are available at any home and garden store, and are simply agarose crystals that expand and store a considerable volume of water. If you are going to breed crickets this is the cheapest option. Using vegetables as a moisture is too expensive and only increases the chance of a bacterial/fungal infection that will destroy an entire colony.
I provide delicups filled with moist, autoclaved soil to the adult insects. It is possible to use unsterilized soil but you'll be unable to recycle it after a few uses. I generally keep 4 soil cups per 5,000 adults and move them out after 5-10 days of continuous egg laying. During this time I generally will re-moisten the soil once or twice with a garden sprayer.
For incubation I transfer the soil cups to larger delicups, stacking them 2 to a large cup. I do this because the room I rear them in has continuous airflow, which sucks out any moisture very quickly. They stay in the giant delicups for roughly 7-10 days, at which point they begin hatching. I transfer all hatchlings to a fresh rubbermaid bin and the cycle repeats.
The photos below illustrate the two stages for Gryllodes sigillatus. Gryllodes are smaller and take longer to mature than the industry stable Acheta domestica but: they are more drought resistant, less noisy, and considerably less smelly. They are the perfect cricket for roughly 95% of all gekkotans.
Remember, you want to keep your adult crickets as hot and dry as possible. Any residual moisture will spawn an infection and kill your colony. Unfortunately, keeping your hatchlings too dry will dry them out and kill them. I cover hatchling cages with syran wrap for the first 2 weeks, after which point their evaporative water loss rates have stabilized.
If you are attempting to produce adult crickets to feed your collection, your cricket farm will take up a fair chunk of space. If you need small crickets (1/4 inch and smaller) to feed small geckos, you could get by with much less space if you're willing to purchase 50-100 adults every week or two.
Good luck.