The key to playing well together is to listen to and watch one another. Learn signals so you know who is taking the next break. Listen for holes in the sound and fill those gaps.

A choir or an orchestra has a director, a band, specifically a bluegrass band (or a jazz band) has soloists. And it is that soloist who is the director at any given moment. As the melody passes from one vocalist to another, or from one instrumentalist to another, so does the attention of all players of the band. The soloist is always right. If the soloist changes the beat, or even skip a beat, the rest of the band must adapt.

Even good bands change their timing. We are all fallible human beings, not machines, but this is what makes music fun to listen to. If you listen closely to recordings of Earl Scruggs and his band you will notice that the band speeds up on the banjo breaks, not a lot but enough to make a listener scooch closer to the edge of their seat. Subtle changes in beat and syncopation are features which can make a performance more dynamic, as long as all the members move together.

Keep the start and the ending of a piece the same. You should do your experimentation in the middle of the piece. It is in the middle section where you can try out various breaks, or improvisations on top of a well-established Um-Chuck, but start strong and end strong with well-rehearsed parts. You may want to have a musical clue that the song is coming to an end, like ending a verse on a high note to signal that the next chorus is the last.

Melody & Harmony:

Singing is good, even for fiddle players. If you want to easily memorize melodies, learn the words. There is a connection in the brain that makes it easier to remember pitches if those pitches are associated with words. When learning a new piece start with the basic melody using simple quarter notes. Make sure you have that melody well understood and well in-grained into your head. Know where the beat is in that melody.

Now start building on that basic melody.
Choirs have 4 parts: soprano, alto, tenor and bass.
Bluegrass is divided up as vocal (alto), tenor (up a third above the melody), baritone (a third below the melody), and bass (an octave below the melody). What is true for vocals, is also true for instrumentation. If you want to play the fiddle to harmonize with a vocal, you do not want to occupy the same frequency as the melody. Move up a third, or an octave, above that melody line.

The fiddle is a melodic instrument, but you can also do chords... in the form of double stops.

You can take a simple piece like "Will The Circle be Unbroken" and experiment by playing up a third from the melody like (like a tenor).
Another option is to alternate the playing of the A part of a tune, where one instrumentalist plays four measures of the part and another instrument completes the part by playing the second four measures.  To make things more interesting you could play a bass line and do double stops. 

To play a simple C chord put your first finger on the D string and third finger on the G string and play those two strings together.
To play a simple G chord put your first finger on the A string and third finger on the D string and play those two strings together.
To play a simple D chord put your first finger on the E string and third finger on the A string and play those two strings together.

If you have more time you can pluck the strings more like a mandolin, but don’t use open strings. The point is not to hit specific notes, it is simply to provide the chuck on the 2nd and 4th beat of each measure.

This has simple chords to it. You can use a I, IV, V chord progression. So, in the case where this piece is played in the key of G, you only need to play a G chord, C chord, and D chord. Eric pointed out that you can get a set of double stops where you do not need to change your fingering much:

Alright, you can play two notes of a chord.  Now what?  How can we make this interesting and different?  One trick we can use is to rock the bow across the strings so as to accentuate the beat:

You can do this simply by rolling your wrist in what is called circular bowing.

Another trick is to slide into the chord when you start playing it. Start flat and sharpen the notes until they are on pitch

Bluegrass (like Jazz) is built upon collaboration, experimentation and improvisation (and a lot of practice). It is good to practice alone and learn to master your instrument from a technical point of view. But learning music is like learning a language, you can only learn so much in a classroom. You learn much more and much faster by being immersed in that language. It’s good to have a bag of tricks you can fall back onto so that as the music progresses you can listen to the other players and react to changes in a fluid manner. And above all, have fun while you are playing.

Playing Together
(with the High 48's)

The High 48's gave a workshop on how to play together as a band.
There are two parts to music - Rhythm and melody
Eric started with the Rhythm:

If bluegrass bands have no percussion, where does the beat come from? ...and bluegrass definitely has a beat. One of the things that most defines bluegrass is that 2/4 Um-Chuck Um-Chuck Um-Chuck beat (although in some parts of Minnesota it is more of an Um-Pa Um-Pa Um-Pa beat - but that is a whole other topic). In the case of the High 48's (as in many other bands) it is the Bass and/or Guitar which provides the Um on the 1st and 3rd beats of each measure. It is the Mandolin (and sometimes fiddle) which provide the chuck on the 2nd and 4th beat of each measure.

The vocalist will provide the main melody (assisted with various instrumental breaks) and the banjo will roll on top of all of this. The first order of business as each musician does their instrumental break is to ensure that the Um-chuck Um-chuck Um-chuck beat is still present.

So, one of the primary things to learn is how to chuck.
Chucking is quite simple. Drop your fingers across the fingerboard so as to dampen the strings. Using the lower end of the bow drop the hairs onto the G and D strings in a muted chop. Make sure the strings do not ring. Some describe it as a crunch.