As always, the first step is to find a treat your dog is really willing to work for! Once this treat has been identified, break them up into small pieces (no bigger than your pinky fingernail).
Essentially when you are teaching your dog a command, you will first teach them the result you are looking for (in this case, down) and once that is learned you are putting a verbal command to it. So to teach the result of laying down, first ask your dog to sit. Then, take a small treat in your hand and put it close to your dog’s nose and slowly move it to the ground towards your dog’s front feet. This motion of moving a treat from your dog’s nose to the floor will almost always result in your dog laying down so he can get to the treat. Once your dog does lay down, give him the treat immediately and praise him! Dogs only have an association period of about 1.5 seconds, so you need to get that treat to him in 1.5 seconds for him to understand that laying on the ground=treat.
Do this about a dozen times or so to make sure your dog is making the connection. Once your dog seems to be predicting what you want when you put the treat out by his nose, add the word “down” or “lay down” (pick one command and stick with it!) into the mix. So every time your dog puts his belly on the ground, say “lay down” and give the treat. Do this a few more dozen times and your dog should have it! Try just holding the treat in your hand, close to your chest, and say “lay down.” If he lays, praise him and give him that treat as soon as you can.
Do not be discouraged if your dog takes a while to catch on, some dogs are better at learning new things than others. Just keep doing each step over and over until your dog gets the hang of it before you move on to the next step. Some dogs figure this out in minutes (like my cavalier) while others take a bit longer (just like my chihuahua mix and border collie mix-they took a few days). My border collie actually hates the command and action of laying down. I have found in my experience that certain breeds are not fans of laying down or rolling over. So definitely be patient and make sure to reward the little victories!
Reminder: dogs get frustrated just like we do, so don’t train with your dog for more than 15 minutes at a time. That way, he can retain everything you are trying to teach him and not get so frustrated that he shuts down and you have set backs.