Watch the Holding & Handling the Bass online guitar lesson by John Goldsby from Upright Bass Handbook
There are two ways to hold the double bass: sitting or standing. In this video course, I'm going to address standing with the bass, and give you some basic ideas about balance, positioning, and moving around the instrument. The back of the top inside bout should rest just inside your hip bone. This resting point, balanced with some light guidance with your left hand (especially your left hand thumb) is all you need to keep the bass in position and anchored securely.
Another important position to check is the height of the bass. I like to have the nut, at the top of the fingerboard, right at my eye level. This lets me play in the lower positions without raising my shoulder too high, and also allows me to move into the higher positions easily. My right hand is at the perfect plucking position at the end of the fingerboard. I see some bassists with their basses higher or lower than this, but in my experience, this is the place to start--with the nut at eye level. The bass is a large instrument, but you should not strain too much to play it. You should play with energy, but play with low stress. When I have the bass resting inside my hip, I can balance the instrument even without my left hand. Sometimes I'll put my left knee on the back of the bass for extra support and balance, but my general playing position is with my weight evenly distributed on both legs.
When I shift positions, my left hand can freely move up and down the neck, even into the high register (what's called the thumb position). You should be able to move your left hand freely, sometimes adjusting the angle of the bass by slightly moving your hips.
My last piece of advice here is to get a full-length mirror and practice in front of it You should look relaxed, and your movements should be relaxed, yet precise. Remember that the motion makes the music. You should be able to hold the bass securely with a minimum of effort, and glide over the instrument to get to any note that you need to play.