Instructions
Bathe and wash your dog every day for a quick 30 points or so.
Take your dog for a walk and hit as many "?" squares as you can manage. Better walks earn you more points and new items.
Enter contests. Winning a contest nets you 100 Trainer Points, but even losing gives you 25. Contests are by far the fastest method for accumulating points.
Perform the "Brush Glitch." Put your Nintendo DS on the charger. Grab the rubber or wire brush item and prepare to brush your dog. Place the brush on your dog's chest, then close the Nintendo DS and leave it for a few hours. You will earn 3 trainer points per minute, amassing hundreds while you do other activities.