Bach's Air from Orchestral Suite No. 3 in D Major BWV 1068 (also well-known as Air on the G String) is one of the most recognizable pieces of music from the baroque era. Although originally written for orchestra, the music is now more well known as a solo violin piece with piano accompaniment, arranged by August Wilhelmj in the late 19th century. When he transposed the original key signature of the music from D Major to C Major, he was able to play the entire melody on the G String, giving the piece its most recognizable title. The tune has been used in many forms in modern film, television, and video games.
To master this piece, you will have to develop the ability to make a good tone through the very long notes, such as the first note of the piece. This will require control of the bow speed, placement, weight, and vibrato. Make sure to save bow right at the beginning of the note. If you start off with too fast of bow speed, you won't be able to keep the note going for the full length. Vibrato will be helpful for this as well because with a slow bow, there is a risk of a rough, choking tone. Adding vibrato will help warm up the sound and help the string continue vibrating. Authentic performance practice of music from this period would be to use vibrato very sparingly, but it has become common to use vibrato continuously in the modern manner of performing. I suggest that you practice your scales with as slow a bow speed as you can so you develop your ability to sustain very long notes.
Another piece of advice is to stay near the tip of the bow after the first long note. Many students aren't comfortable playing multiple notes near the tip of the bow and will instinctively move to the middle. The problem with this is that you have to play a very long up bow next and its better to start right at the tip. There are several other spots in this piece where you need to pay attention to where the long notes are and get to the tip or frog ahead of time, so plan ahead for where the bow should be.