An anonymous poster asks how Dozer learned the names of his toys. It's a really good question, since this particular skill can be expanded upon in a variety of ways (such as when we ask Dozer to find and put up his toys).
To put it simply, we never formally taught Dozer the names of his toys. But Dozer spends the vast majority of his time with us, and we speak to him constantly; he is utterly selfish, and will eagerly learn something that he might use to gain food or entertainment; and he is extremely toy driven.
Very early on, I spent a lot of time saying the name of each toy whenever we played with it. Sort of a nonstop babble: "Oh, you brought the rope. What a nice rope. Whose rope is that? Is that your rope? Let's play with the rope. Get the rope. Yay, rope! Rope! Where's the rope?" Like that. After a while, he started connecting each name to each toy.
After extensive name-toy-name-toy associations, it's time to firm up those associations. The easiest way to do that is to ask the dog to bring a specific toy. So at playtime, I ask "Where's the [toy name]?" This is Dozer's cue to find the toy I'm asking for.
He gets nothing whatsoever for bringing the wrong toy, and sometimes I even get up and walk off, the most boring result ever. Since he tends to persist if he thinks some toy might work, I will often give him negative feedback like "uh uh," just to reinforce the idea that the wrong toy isn't going to get him squat.
I respond very positively--praise, treat, petting, or playing--when the requested toy appears.
So you can see that it is to his advantage to learn as many toy names as possible. Consequently, his vocabulary, as it applies to toys, is very large.
Of course, it takes time for a dog to learn all the names of its toys. Dozer has spent a lifetime perfecting his understanding. He learned the first toy names gradually, through a process of trial-and-error. Now that he knows all his toys' names, he learns new toys' names through a process of elimination.
Now, this is in contrast to Felanie, who was not really very toy-driven at all, and was not a "mouth" sort of dog. She would rarely pick things up on command, and my request for her to "pick it up" was often met with an incredulous stare. "You want me to what? That nasty thing in my mouth? Riiiight." Of course, maybe the fact that Dozer would immediately bulldoze her over in his haste to respond to my command (never mind that it wasn't a command given to him) had something to do with her disinterest in fetch-type games.
My point is that not all dogs are going to learn these types of skills easily. It depends on your dog's personality and motivation.
I think most dogs learn the names of their toys rather informally, through a process of trial and error, rewards and no-responses. However, formal training is also possible. The keys are consistency in commands and names (you can't say "Get the octopus" one day and "Fetch Mr. Tentacle" the next); teaching logical precursors (first teach dog to "pick it up" or "get it" or similar commands that are not geared to a specific object, spend a lot of time playing with dog and toy and saying toy's name at same time); baby steps (teach one toy name at a time); and consistent and prompt rewards for correct responses, no-response or negative-neutral-response when incorrect.
(On a side note, Dozer finally confirmed, to his satisfaction, that he really does have to put his toys in the toy box to get a treat; lately, he'd been experimenting to see whether the toy could be up against the box but not necessarily in the box. We're still working on the part where he pulls the toys out of the box right after dropping them in. I think the process of putting the toys away just makes him want to play with them all.)