i try to think of anything that helps me and is also fun for my pup. also, any behavior that your dog is just inclined to do that you can twist a little to suit your needs are good. example: my Sadie LOVES to pick up pieces of paper in the house and in the yard. At first she'd tear them up into confetti, but i quickly learned that i could "trade" her a tidbit, some praise or a toy for her trash and she was happy, and i got all my trash picked up. Now she just picks up trash and brings it to me. I also am working on getting her to help me gather the stray laundry. I frankly don't think i'll ever have any success with "go fetch my slippers", but i hardly ever wear them anyway
it's all about what you feel will help you or things you want your dog to learn. I've taught Sadie left and right, upstairs and downstairs, and "go get in the tub" (handy now that she weighs 70 lbs- i don't have to wrestle her for a bath) - although now getting her OUT of the tub is more the key thing
the only advice i can offer with "lay down" is to start that one after your dog has a good grasp of sit. once they'll sit anytime, anywhere, put them into a sit, show them a treat in your hand, and then place your hand on the floor with the treat under it- close to their front paws. they should almost naturally go onto their elbows to try to get the treat- lift your hand to let them have it and give lots of praise. gradually, you'll make sure they're fully laying down before you release the treat, then make them lay longer and eventually you'll ask your dog to lay down without having to put the treat on the floor, and you'll ask them to lay down and then give the treat from your pocket (or wherever). Personally, i've found that "go lay down" is convenient if it encompasses a completely different concept. i use the command "down" for basically drop where you are, and the hand signal i use at the same time is just palm facing the floor and a push down motion. "go lay down" is more of a directional command, so i use a sweeping arm motion with a pointed finger- the finger tells them which direction to go, and the sweeping arm indicates the "go" action. this has always worked well for me and Sadie caught onto the "go" part almost immediately. i didn't have to get up from where i was when i gave that command, she just followed the direction of my arm and after i asked a couple of times she just went. i figured that laying down once she was out of the dining room was up to her...I use the command "go get in your bed" for times that i don't mind if she's in the same room but i want her out of my way (bed is in teh corner of the living room) and "crate" for when i really want her IN her crate. both dogs are also trained to "get out of the kitchen" if they're underfoot while i'm cooking or putting away groceries. (p.s. training your dog to help you carry in groceries is also pretty handy)
some other mind stimulation games i have used include teaching your dog to identify objects, like ball, bear, frisbee...and asking them to retrieve the correct object from a group of objects or from their toy box. also, teaching your pup to pick up their own toys is a nice bonus. as far as object retrieval goes, you could always teach your dog to find certain of YOUR objects- like the phone, tv remote, purse or wallet. I was thinking i'd teach my dog to get a bottle of water from the fridge, but then i realized that would give her the tools to access the freezer, and access her favorite things- ice cubes, and i didn't want my ice supply permanently slobbery, so i decided to skip that trick. it might work for you though if your dog isn't an ice cube junkie- just make sure to fasten a towel or rope to the handle of the fridge so they can pull the door open, and make sure you teach them to close the door once the water/juice/beer is removed. I had heard of a couple who had 2 dobermans who taught their dogs to get water bottles from the fridge, and the dogs were constantly getting themselves fresh water late at night...so use that trick at your own risk! other tricks include- Open the door, shut the door, wave, high five, speak, roll over, even the cliched play dead...really any new trick is going to engage your dog's mind, and if you can use those words/tricks every day you will be constantly stimulating your dog's mind. giving your dog directions is also good for mental stimulation....something akin to a mental agility course, or the kinds of directions that cattle herders give to their dogs...any dog can take directions. we haven't gotten that far with Sadie yet LOL
you can also get a ball, i think Kong might make it, that you put some food or treats in, and your dog has to figure out how to roll it just right to dispense the food. those are pretty good if your dog really does have boredom issues, like while you're at work.
Hubby and I sort of are taking our cues from the childrens' book "i'll teach my dog 100 words" as well as all of the useful things that service dogs do for our pup's training. i made her a backpack to carry her own water, etc on walks
the big key to training "tricks" or things like "lay down" is to figure out what motivates your dog. Sadie will do ANYTHING for a biscuit, so we use pieces of biscuit to train her. (get in the tub was easy, just toss in a biscuit, tell her to "get in the tub", praise like crazy once she was in there LOL), but not all dogs are so food motivated. If your dog likes a few min of play time with a fave toy, use that. lavish praise is also a good motivator. i know for a fact that my husband thinks i'm insane when i tell Sadie over and over what a good girl she is laying down or in the tub, but he can't argue with the results! so far the longest its taken her to have the lightbulb go on has been 2 lessons
also, sometimes if your dog is older, they will refuse to lay on the hard floor. if that's the case, make sure you're asking them to lay somewhere comfortable for their joints
good luck!
