Teaching a stay
Remember you must utilize a release cue.
Stay behavior works with Distance and Duration.
Put your dog in a sit directly in front of you.
Show your dog a flat "cop" hand with no treat.
Wait approximately 2 seconds then release your dog to move away from the sit location with a treat when you release them with your verbal release cue "OK".
If your dog breaks from the sit position, make sure you're not inadvertently luring them away from that position but immediately put them back in a sit and then release them "OK" after about a second.
Slowly build up the amount of time your dog will stay sitting directly in front of you. When you can have your dog sit for approximately 15 seconds then you should begin moving away from your dog a step at a time.
Each time you increase the distance away from your dog you should reduce the amount of time you ask them to stay.
The goal is a 30 second sit/stay.
The Down stay should be taught in the same way as the sit stay. Lure your dog to a down, slowly stand up and stand in front of your dog for a few seconds then release them "OK".
Once you can easily down your dog and stand up without them breaking position you can begin adding distance to your stay behavior.
The goal is a 1 minute down stay.