You can see all the charts and data Brooks Baseball provides here. I'll go over the ones that are easier to understand (for me, at least) below. For all images, click for a larger version.
This chart gives the speed of each of Samardzija's pitches. As you can probably see, he started off almost exclusively with fastballs to get himself adjusted. Then, he alternated fastballs and breaking pitches (sliders and changeups, according the MLB Gameday) over the rest of the appearance.
He was in the 96-98 MPH range with his fastballs, topping out at 99. His breaking balls were all right around 84 MPH. If he can keep that 10+ MPH difference between his fastball and his changeup, he'll be quite effective.
Next, here is a plot of balls and stikes. The blue points, labeled "X", are balls put in play.
As you can see, Samardzija pounded the zone pretty well for most of the outing. The extreme outlier was a pitchout/wild pitch. This graph is from the catcher's point of view, meaning that that pitch was high and outside to the left-handed batter.
Here's a graph of Samardzija's release point from pitch to pitch. Having a consistent release point is important for all pitches. If Samardzija had a different release point for his fastball and changeup, for example, batters could pick this up and know when each pitch is coming. Since the main purpose of a changeup is to look like a fastball, this would completely destroy the effectiveness of the pitch.
Samardzija had a consistent release point across all three pitches, which is a plus. The one outlier, I believe, is the pitchout - so absolutely nothing went right there.
This one shows the speed of pitches color coded by result - ball, strike, or in play. The gap in data represents the bottom of the seventh, when the Cubs were at bat. This chart more clearly shows how Samardzija started with just fastballs, then mixed it up, then went mostly offspeed in the eighth.
I'm not sure how much information you can get out of these last two (it's possible that someone can't, but I can't). They are interesting to look at, however. These graphs show how, on average, each type of pitch breaks. The first is an overhead view, as if you were in the blimp with Samardzija at the top of the graph and home plate at the bottom. The second is a side view with the pitcher on the right and home at the left (in other words, as if you were sitting on the first base side).
What can be learned from this? Well, I'm sure quite a bit, but here's what my simple mind picked up: First, Samardzija pounded the zone, showing he wasn't afraid to throw strikes. Second, he had a consistent release point for all pitches, which is a positive. Third, knowing he was only going to throw a few innings (he was a starter in the minors), he was able to max out and throw his fastball in the high 90s, another positive. Finally, his breaking stuff was 10+ MPH slower than his heater, meaning that those pitches will be very effective at keeping batters off balance.