You need at least one accessory in with your items.
Basically, when you take a dog for a walk, plot a route preferably going through as many ? icons as posssible, but you can choose what you want to do. The last part of the walk must go to one of the parks, then back home.
When you've arrived to the park, go into your bag, then into accessories and change an accessory on your dog, then go Back out of the accessories section. The game should save at this point, after it's done saving power-cycle your DS, go back into nintendogs. You should be back home at this point, and you have items you got on the walk and you can go straight out on another walk with that dog.
How it works:
The parks share some (maybe a lot of) code with your house (the touch screen contents are the same, and you can access your items, the only difference is the picture on the Top Screen and the item to Save is replaced with the icon to go Back out of the park). As said, you can access your items in the park, and change accessories. And you can't (shouldn't be able to) save in the park, you can only go out of the park instead.
Let's look at another area of code: the items list, namely the accessories. If you change an accessory on a dog and go back out of the accessories, the game saves automatically (don't know why this is)
Put two and two together, hmm .. you can save in the park ? And your in the middle of a walk, so in the save file there the bytes to stop a certain dog going out on a walk for x amount of minutes do not exist (probably just 00s). Also, the items you have collected on said walk already are saved to the save file.
So you've saved the items to the save file, and 00s where the bytes to prevent a certain dog going out on a walk would be if you had just continued on your walk and saved afterwards.
We know this has happened, so we do what any good glitchologist would do and reset the game .. making the game load our save file that shouldn't have been saved in the first place..
..and the best part about this is you can do it over and over and over again :)