A circle of couples, every other couple facing along and against line of dance, forming sets of two couples facing each other.
The Figures
Forward and Back (4 bars): Advance toward opposite, and retreat.
Turn Opposite (4 bars): Advance to opposite, turn opposite, and retreat.
Balance to Partners (4 bars): Advance toward partner, and retreat.
Turn Partners (4 bars): Advance to partner, turn partner, and retreat.
Ladies' Chain (8 bars): Ladies take right hands and cross over, giving left hands to their opposite, who turns them by the left to face in again. Repeat to return home.
Forward and Back (4 bars): Advance toward opposite, and retreat.
Forward and Pass By/Through (4 bars): Advance to opposite, and pass by/through to the next couple.
Creative Interpretation
The simplicity and vagueness of the descriptions open the door for lots of creative interpretations.
For example, how shall we interpret the instruction to "turn"? Most groups I've seen take both hands and turn clockwise, but that's by no means the only option. It could be a turn by the right, or a turn by the left, a counterclockwise turn with both hands, or even a dos-à-dos. (Based on the description, the latter is less likely—if it were a dos-à-dos it would've say so—but at this point, we're going for creativity.)
Likewise, how shall we interpret the instruction to "pass to next couple," "pass by to next couple," or "pass through to next couple," as it is variously described in the sources? Several options come immediately to mind: 1) pass by to the left, Follows passing right shoulders, 2) pass through, Leads on the outside, Follows on the inside, 3) the first couple (facing line of dance) pass through on the inside, between the second couple, 4) vice versa, 5) the first couple raises their inside hands in an arch, and the second couple passes through, as in the Sicilian Circle, 6) vice versa.
The Music
The fiddle tune of the same name would be an obvious choice, but really any square, energetic, walking-tempo tune will do. There's lots of room for creative interpretation here too.
The original fiddle tune is a reel in 2/4, so "4 bars" above can be interpreted to mean 8 counts.
Forward and back, forward and again and pass to next couple (as in the Haymakers).
Soldier's Joy (Tousey & Small, 1878):
Form as for the Spanish Dance [not described in this source].
All forward and back, swing the opposite—all balance to partners, and turn—ladies chain—forward and back, forward again and pass to next couple.
Soldier's Joy (Schell, 1890):
Form as for Sicilian Circle.
All forward and back (4); turn the opposite (4); all balance (4); turn partner (4); ladies' chain (8); forward and back (4); forward, and pass by to next couple (4).
Soldier's Joy (Elmwell, 1892):
Form the same as for Sicilian Circle [not described in this source].
All forward and back (4); Turn the opposite (4); All balance (4); Turn partners (4); Ladies' chain (8); Forward and back (4); Forward and pass through to next couple (4).