Each NPC companion in Dragon Age has an approval rating that will change throughout the course of the game based on the decisions you make. For example, choose to spare Zevran's life and invite him into the party, and Alistair won't like it one bit.
If their approval drops too low, they can even leave the party. And while approval isn't too important on some companions, like your dog, other companions may have quests or be able to teach you skills if you get their approval rating up.
So what do you do if your decisions have made them upset? You bribe them with gifts. Unfortunately, Dragon Age doesn't make it very clear on how to go about giving a companion a gift. Fortunately, it is actually quite simple once you learn the trick.
To give a companion a gift, simply select that companion and then go into the inventory screen. Right click on the gift and hold down the right mouse button. You'll see the icon to give as a gift on the left side of the radial menu that pops up.
It's that simple. Just remember, you can't give a gift while your main character is selection. You have to go to the character you want to give the gift to in order to do the gifting.
Yes, the entire process is awkward. The inventory interface is one of the few flaws in Dragon Age.
Now, what to give? Check out the Dragon Age Gift Guide.
Dragon Age Information
Dragon Age Tips and Strategies
Dragon Age Companion Guide
How to Unlock Dragon Age Class Specializations