trick suggestions & teaching "down"

Before you can teach "down" you must have a very reliable "sit." 

With the dog in the sit position, tell them "down," with a treat in you hand, as you say down, bring the treat down towards the dogs front feet, the dog's head should naturally go down to where the treat is.  When the dog's nose is on the treat, drag the treat forward, away from the feet, and place the other hand on the dog's shoulders or bum, to prevent it from standing up.  Don't muscle the dog into position in any way, that hand is there just as a gentle guide.  The only way I could get my 6 year old adoptee into a down was to have him sit, tell him down, with the treat in position, when he'd put his head down to see the treat, I'd let him grab a piece of the treat in his front teeth and then pull it forward, and down he'd go.  If he didn't have the treat in his teeth, he'd just look at me like WHAT DO YOU WANT ME TO DO?   Sitting on the floor with the dog can make this easier.  Good luck!!!

Yup, thats how we taught our girl in doggy class. One problem she had was kinda my fault. First I taught her "sit down" then I tried to go to "lay down" and I think since they both had "down" in it that she thought sit down ment lay down so I had to do a quick reform and make it "sit" only and "down" for lay down.

You can try teaching her play dead.  After she has learned down, proceed by turning her onto her back while saying play dead and hold the treat infront of her nose.  I say "okay" for them to get up again but you can choose not to do that if you wish.

Stay is also very important if she hasn't learned that already.  And depending on what breed she is, you can teach her to stand on her two hind legs.  Small dogs can do this fairly easily, but I wouldn't try it in a large dog.  It's harder for them to balance themselves on two legs and you probably dont want to encourage a dog that big to stand up taller than you.

Another trick I taught our pom is to "crawl".  I put him in a down then placing one hand on his back, leads him with a treat in the other hand.  We're still working on this one.  Now he can crawl without my hand on his back.  I'm hoping we can get to a point where he'll follow me crawling as I walk, or crawl to a treat placed on the floor.  I must say it's awfully cute watching him though.

One thing you might try is putting the food under a chair, your dog will likely get down to crawl under the chair for it, then you've got your chance to name it and reward it.
 
Or to introduce a hand signal, and a verbal down command at the same time - from in front of your dog, leash and cookie in the left hand, your right hand signals like a policeman's stop signal, then you lure your dog down with the left hand. If your dog doesn't follow the cookie to the floor and drops his front and hind end, you can use the right arm to gently position him.

You can also sit on the floor, make a little "bridge" with your leg, and lure the dog under it with a really good treat.  Once she's down, say "down" and open your hand, letting her have the treat.
Or, you can carry Cheerios around in your pocket.  When you see her lie down on her own, "capture" the behavior by saying "down", and giving her a Cheerio.