For orbit, try thinking of it this way...
First simplify from three dimensional space to a 2 dimensional plane, say a sheet of paper.
Also for simplification, we will consider the case of one large object and one small object. We will consider the large object to be 1) not moving and 2) so much larger than the small object that the large object is essentially unaffected by the gravity of the smaller object.
The small object is already in motion, traveling along in a straight line, but not directly at the large object, just right past it.
Now lets introduce gravity. What will this do to the motion of the small object?
It will accelerate the small object in the direction of the large object.
If the object was traveling towards or away from the large object, it's existing velocity would be affected. But, since the small object has velocity parallel to the large object, that velocity is not affected by this acceleration, instead it is pulled from it's straight forward path in the direction of the large object while maintaining speed.
We see this as a curving of the path of the small object towards the large object.
Basically, it is the existing velocity of the object that keeps it from falling into the larger object and the gravity is what is keeping it from just flying off.