Welcome to PoA and Flying!!!! Having learned in a DA20 myself, I know where you're coming from.
Steering a Diamond 20 on the ground with its castering nose wheel isn't something I would expect for a brand new student to get their head wrapped around within the first lesson or two.
With other aircraft and steerable nose wheels (like Cessna and Pipers), maneuvering on the ground is something that might come along a little faster. But Diamonds and Grummans take a bit more time to figure out.
The good thing is, once you figure it out, it's very simple to do.
The simplest way is to do a lesson where a significant portion is just taxiing. Just "drive" all over the airport learning how much input is needed on the rudder to turn, and how much added braking is needed to increase the rate of turn and reduce the turning radius. Sometimes adding a bit more power to "pull" the aircraft around is needed.
But if you ask the instructor to permit more time learning to taxi, he or she should be willing to accommodate the request.
And there is no real video showing the operation of the DA20 brake system. The simplest way to describe it is that the left brake pedal is connected to the brake on the left main wheel. Push with the brake pedal your left foot, and you will swing to the left. Same goes for the right pedal. Push that with your right foot, and you will swing to the left. Press both at the same time to come to an even stop.
Keep in mind that using brakes to turn a DA20 are not always required. They help, but the location of the rudder in the slip stream of the propeller is often enough to turn the aircraft when you press the rudder pedal. Then add just a small touch of brake if you're not turning fast enough.
As with all the skills, it's practice practice practice.
Again, welcome to PoA. Feel free to post other questions.
And look for ARFlyer (Andrew Finne) to post. He is in your region and is a good person to link up with.