MILLSCALE,
A very broad subject.
Every project and weld bead or pass is unique like the proverbial snowflake.
1) When is grinding necessary?  When flaws or excess metal are present that will affect the required quality of the completed weld.
2) Is it really necessary to grind?    Not always!  My philosophy is to limit grinding to it's absolute minimum.
3) Any tips on how to minimize the grinding? 
  a) On the internal beads, keep the profile as flat or slightly concave as is possible. Try to work the sides of the bevel so there aren't any wagon tracks. Convexity is your enemy down in the groove.
  b) When ever there is a problem, STOP! ASAP! Fix (ie. grind) adjust and carry on.
  c) I try to start a new pass before Top/Bottom Dead Center with minimal build up until the center and then maintain the depth of deposition as evenly as possible. This way there is less of a "lump" at the start.
  d) At the Top/Bottom, gradually taper off the thickness of the bead as you move past the center point.
The "c" and "d" above is what has worked for me to keep my layers an even thickness around the pipe and minimize grinding at the stops and starts. As your skill advances, there will be less and less grinding and you will develop your own tricks through minor, almost imperceptible manipulation techniques that are all your own. Eventually, you will learn what does and does not Require the grinder.
Hope this makes sense and helps.

For stick I like to feather before doing tie-ins on the root.  For restarts, I like to start 3/4" or so behind the keyhole and then drop in once I am up to temperature.  After doing this I like to knock out the bumps that result from this restart technique.  Same deal for wire.

For TIG I like to feather before doing tie-ins on the root so that I can keep the fill rod tangent to the pipe during the tie in, although it really isn't essential.

Other than that I don't know a reason to be running a grinder once the welding starts unless a mistake is made.