Haymitch's initial approach is gauging their individual abilities. He starts off by telling them that he's considering training them separately, but when they refuse, he begins determining what skills they have that may be useful in the arena; in this case, Peeta's strength and Katniss' aptness with a bow.
On top of this, Haymitch tells them not to reveal their capabilities while in the Training Center; instead, try and become proficient in some other trade or tactic. He suggests learning snaring, throwing spears, swinging maces, and tying knots while saving their true skills for the private sessions.
Finally, Haymitch instructs that they need to stick together, no matter what. This holds true for both during training and during the Games, ultimately developing into the "love story" that keeps them alive throughout the rest of the book.
Hope this helps!
