I'm not sure what you're using for motion tracking, but I know that if you use after effects you can set a nice place of high contrast to track and then if the action gets insanely shakey you can shuffle the footage to the place where the mark went off and re-put it where it needs to be.
other then that combine these methods :
1) When you can stand still, do. While standing still make sure to make a triangle out of your two hands holding the camera and put your elbows against your torso to help steady everything(don't use the LCD, use the viewfinder). Or as suggested use a MONOPOD(not a tripod, as a monopod is much better suited for quick use where you'll need to set up and film quick).
2) when you have to move, move enough that it will look good as a cut point.
3) Never move the camera! think of everything in pivot points. Pivot your entire body left or right smoothly to follow action that you want to cover that is moving out of shot. Pivot at the hips smoothly to go up and down with action.....this is all if your not using a monopod. If using a monopod you should still think in smooth pivots though, but of course they don't involve you gyrating at the hips or anything lol.
If you want to get fancier you either need to get equipment that can assist you.....or learn to dance. seriously! You need grace, balance, flexibility, and tempo to do anything advanced with a camera....and without alot of practice at something like dancing you'll never move beyond the basics without making the footage look horrible.
One last thing you can do all low core is head to the hardware store and build a T section onto the bottom of your camera so that one section goes straight down towards the floor and at the bottom is some weight...then theres the other part that makes it a T which you hold.....the weight/pivot forces a smooth movement....look it up on google with keywords like "Home made steadicam" for in depth plans.