From this article:

Given her connection to the film, Lorig was one of six Olympians featured in a recent Glamour spread. The Olympic archer, together with a few of her fellow female archers, will also grace the cover of an upcoming special-edition "Hunger Games" DVD.

"She was lovely," Lorig told the Associated Press. "We had a great time coaching and working together."

To prepare for her role as "Hunger Games" heroine Katniss Everdeen, Lawrence trained with professional archer and Olympian Khatuna Lorig to learn how to properly shoot with a bow and arrow.

A detailed rundown of her skills can be found in this article from a professional archery website. They go through various aspects of Lawrence's shooting and give it a verdict "Real or Not Real" (a Mockingjay in-joke):

We know Jennifer Lawrence’s original archery coach was Khatuna Lorig, a five-time Olympian and Olympic medalist who clearly taught her how to shoot well. However, we also know Hollywood takes liberties with shooting form. So, are Katniss’ archery techniques real? Do they line up with the steps of shooting that USA Archery teaches? Let’s take a look.

Stance

The “Catching Fire” archery simulator scene shows Katniss’ feet slightly angled toward the target, with her front foot slightly behind her rear foot, giving her an open stance. Verdict? Real.

Nock

Katniss nocks her arrows – meaning that she fastens them safely onto the bowstring – superfast. We’re not sure if she double-checks to ensure whether the arrow is correctly aligned, or if the arrow is snapped onto the bowstring (nocked) in the correct place. Verdict: Undecided.

Hook and Grip

Katniss has her knuckles curled around the bowstring, which is not correct; the back of her hand should be flat and relaxed, and the bowstring placed closer to the first joint of her index, middle and ring fingers. Her grip – the hand that holds the bow – also shows a finger on the arrow, which isn’t safe. We’d change this part of her archery techniques. Verdict: Not real.

Posture (Set)

Jennifer Lawrence has beautiful red-carpet posture, and it shows when she’s in character, too. Her Katniss has a flat back, low shoulders and she usually appears to be in good alignment. Verdict: Real.

Raise Bow (Setup)

In archery, setup is the act of raising the bow. Katniss raises that bow fast, but then delivers a knockout punch. We’d tell her to slow down, but otherwise, Katniss’ setup is a good start. Verdict: Real.

Draw

We’d love to see Katniss raise the bow and draw the bowstring back more slowly, with a smoother motion. That would help her to keep her upper body in better alignment, and give her a stronger shot. Verdict: Real … but needs work.

Anchor

With a longbow (the bow type Katniss shoots), archers usually pull the bowstring back to at or above the corner of the mouth. This is called the “anchor point.” Katniss uses the under-the-chin anchor point commonly used by Olympic recurve archers, and we often see her drawing the bowstring past her anchor point, which is a no-no. Verdict: Not real.

Transfer

Once she’s reached her anchor point, we see Katniss pulling her elbow just a little farther back, transferring the bow’s weight into her back muscles before she shoots. Verdict: Real.

Aim

We can’t be certain when Katniss starts aiming, but top archers do not aim until they have fully drawn, anchored, and transferred the bow’s weight into their backs. Once they’re fully aligned, they aim for two to three seconds. Verdict: Real…we think.

Release and Follow Through

Coach Khatuna Lorig said she worked on this with Lawrence, and it shows. Katniss keeps her draw hand near her face and neck as she releases the bowstring, and follows through with strong back muscles. Verdict: Real.

Overall? Lawrence’s Katniss is the real archery deal. We would encourage her to slow down when possible because resting between shots is essential for strength and good shooting. But who are we to argue with a woman who shoots explosive arrows into the sky?