Jordboss's post is correct for the earlier Connections (V1, V2, V3, V4 and V4.5) but if you're talking about another version:
V5: You're talking about Bonding, not training. Bonding occurs on even hours of the day (10 AM, 12 PM, 2 PM, 4 PM, 6 PM), and your Tamagotchi will beep when it needs you to select the Training icon and select an item. You can cheat by setting your Tamagotchi's time to one minute before an even hour.
V6: This does not have a training bar, but even so give it a time out when it refuses to do something and praise it when it performs well in a concert or practices its instrument for long. Praise is also a good way of lowering stress; each praise takes away 3 stress points.
Tama-Go: I'm not sure if this one cries like Jordboss said, but if it does, praise it. If it calls for no reason, give it a time out. If it does the wiggle dance (you'll recognise it when you see it) quickly select the toilet icon.