I use two large tanks (24x15x20", WDH), one for adults and one for grown on locusts that are near adults.
Once the Locusts have turned to adults they get moved into the adult tank to replace any that have died off.
Both tanks have full vented lids and egg cartons inside for extra ground space and to hang from during moulting.
I use a reflector bulb pointing down at one end of the tank to simulate sunshine and heat mats underneath and around the edges of the same end of the tank, the bulb is on from 6am to 8pm and during the night the heat mats do the work.
This holds the temperature at about 28c-30c 24 hours a day with a day/night cycle.
Keep the humidity as low as possible, which the full mesh top will help with.
I feed my Locusts on bran and veg, any veg that I feed my BD's on is good,I make sure they they never run out of food.
I don't provide my Locusts with a water bowl, I've found that they drown and are perfectly OK with water obtained from their veg.
Providing the temperatures aren't too cold I have found that adults will mate without any help.
Provide a few tubs with 10cm (4 inches) of soil for egg laying,ice-cream tubs are good for this, position these tubs over the heat mats and keep the soil moist but not soaking.
You can remove the tubs to separate incubating tanks if you want to (incubate at 28c) but I don't have the room so I leave them in with the adults and they do fine.
You should be able to see that eggs have been layed because there will be holes in the soil where the Locust has pushed the entire rear end if its body into the soil to lay the eggs, you may also see "spiderweb" looking white stuff on the surface of the soil, this comes out with the eggs and is normal.
Once the eggs have been layed it usually takes around 10 days for the baby Locusts to start digging their way out of the soil, I then collect them and keep them in cricket tubs with a piece of egg carton and feed them the same as adults.
Once the babies have got bigger they are either fed off to my animals or put back into the tub to become adults and lay their own eggs.
These are only my own methods which I have found to work well and may or may not work for others.