Shade moving
If you want to move a Shade a long way, the best options are a Banshee or Scorpion. With a Banshee the fastest way to cover ground is to use a combination of blasting and ramming, in which you repeatedly blast the ground just in front (be careful not to get too close) then quickly and aggressively ram it while it's still in motion and while your fuel rod gun is recharging. By including ramming you can cover ground over 50% faster than using blasting alone. If you can manage to get partly under it as you ram, so much the better, but you'll have to catch it in mid-air for that. You can get some impressive distance with a good bit of mid-air ramming, and it's possible to keep the Shade airborne with multiple contacts by trying to fly just behind and underneath it. For mid-air ramming it'll help to already be moving towards the Shade as you fire, and obviously you'll want to get the Shade sent up a good way off the ground. See BCM45 for some good examples of this.
A Shade can also simply be pushed along by a Banshee, but push between the front legs for greatest stability. If you push from the side it's liable to topple over.
As for the Scorpion, blasting is an option but the most efficient technique is pushing. The Shade gets nicely caught up in front and you can trundle along at a decent speed, though you may need to slow down occasionally to stop the Shade slipping underneath. Pushing with a Scorpion is slightly faster than using the Banshee's 'blast and ram' method (unless you're good at mid-air ramming perhaps) and you also don't have to be so busy on the controls. You don't need much skill, just a bit of finesse.
A Shade can also be pushed along by a Warthog but it's rather awkward to keep the Shade in check, and you can expect it to be considerably slower than using a Banshee or Scorpion.
Grenades and rocket blasts can send a Shade a decent way of course - while your ammo lasts. Melee can move a Shade but only a tiny amount at a time, so it would be pretty painful to take it any significant distance. It's mainly useful for making small adjustments of position. A plasma pistol or assault rifle are handiest for this as they whack the fastest.
Pointing it
If you want the Shade to point in a particular direction, its base can be rotated by nudging one of the legs with the nose or leg of a Banshee.