Trainer points are rewarded for taking them to contests, and generally taking care of them. Some general activities that earn points are:
- Walks (50)
- Finding a present on said walk (15)
- Visiting friend (20)
- Place in competition (100 - 75 - 50 - or 25 for just entering)
- Petting, Feeding, Brushing and Bathing also reward points.
- When your dog meets another dog and they like eachother (50)
In order to maximize points ensure to always enter the competitions and train your dog well. Taking care of them daily (washing, petting , feeding) will obviously make your dog happier and will reward you more points for things you may miss in a day. This link has a pretty good list of ways to get trainer points and money. There is a trick on here, I haven't tried it (since I've only seen my cousin playing) that if you leave the brush on your dog overnight it will net you a ton of points -
"Brush one of your dogs with a rubber/wire (whichever is nescessary) brush and leave the brush on the dog when you go to sleep. Leave the charger in your DS. When you wake up in the morning, go to your game. You will have around 800 training points or maybe more than that."