[Babcock_Hall]

I have read a few pages in several organic laboratory textbooks on this subject, but I am not certain of one or two things.  Shaking for about a minute is sometimes recommended  Agitating vigorously enough for the layers to mix but not so vigorous as to create an emulsion seems reasonable.

My question is how to shake.  I can picture moving the funnel from left to right and back again, moving the funnel closer to and away from my body, and mixing by inverting the funnel.  Is there one preferred method?  I have used the first two methods before, but not the third.

[discodermolide]

I think it's what you feel comfortable with.
Not too near your body incase the funnel breaks and you get covered in the stuff. Arms extended and shake

[IsotopeBill]

Keep aware of how far the stem of the funnel protrudes:  you don't want to clip something and snap it off (done that).  Also, some solvent mixtures are more prone to emulsification than others (dichloromethane/water, for example).  There are various tricks to remove emulsions, such as adding some brine, a very small amount of acetone, filtering through celite before attempting to separate, among others.
  I tend not to agitate too vigorously, but enough to get efficient mixing.  Repeated inversion and gentle shaking/swirling is usually sufficient  Don't neglect to vent, especially with volatile solvents such as ether

[Med90]

it depends upon how you feel comfortable.
If you want plz go through this post on liquid-liquid extraction method.
http://www.medchemblog.blogspot.com/2012/06/how-to-do-work-up-using-separatory.html

[curiouscat]

I've a (perhaps silly) question. During workup, why isn't the solvent-agitation-mixing completed in the reaction flask itself. There's probably a stirrer there already. And then use  the funnel only for the separation? 

As an engineer I've grown used to thinking as mixer-settlers to be two separate vessels.   

[DrCMS]

I've a (perhaps silly) question. During workup, why isn't the solvent-agitation-mixing completed in the reaction flask itself. There's probably a stirrer there already. And then use  the funnel only for the separation? 

As an engineer I've grown used to thinking as mixer-settlers to be two separate vessels.   

In a pilot plant/production reactor I would do the separation in the reactor but unlike lab flasks they have a bottom outlet valve to run materials out off through a sight glass. 
In the lab you could mix in a round bottomed flask  but you'd then need to pour it out into a separating funnel and allow it to stand again so why not just do the whole separation in the separating funnel?

[curiouscat]

In the lab you could mix in a round bottomed flask  but you'd then need to pour it out into a separating funnel and allow it to stand again so why not just do the whole separation in the separating funnel?

No strong scientific reason; yet apparently lots of things tend to go wrong (see warnings above) once people start to enthusiastically shake away liquid filled large glass objects in a crowded lab.