They were organized sometimes by a committee, or sometimes by a local entrepreneur. Local Assembly Rooms in Stamford, Lincolnshire were built by the local dancing master, Askew Kirk, on land leased from the Earl of Exeter( who owned the Burghley estate nearby (Immortalised as Rosings in P&P3).

Indeed it was a condition of his lease of the land that he had to build an assembly room on the site. It was thought that buildings such as assembly rooms, which encouraged social interaction between the marriageable in the locale were an advantage for the small market town.

(All information courtesy of the archives of the Stamford Museum) Mr Kirk acted as Master of Ceremonies at the assemblies there, and, of course, gave dancing lessons to nearly all the local people who wished to take part

As to who paid for what and when, let’s have a look at the text of a poster advertising a series of subscription assemblies at the Assembly Rooms at Newcastle (where Lydia and Wickham ended living at the conclusion of P&P).

The First of the 
SIX SUBSCRIPTION ASSEMBLIES

Will be on THURSDAY 12thJANUARY 1792

The SECOND on THURSDAY 2nd FEBRUARY

The THIRD on THURSDAY 16th FEBRUARY

The FOURTH on THURSDAY 1st MARCH

The FIFTH on Thursday 15th MARCH

The SIXTH on Thursday 29th MARCH

LADIES’ TICKETS for the Season 10s 6d each 
GENTLEMENS’ “””””””””””””””””” 15s

may be had of Mr GRIEVESON at the ROOMS

N.B. Tickets not transferable, and unless there are FORTY subscribers there will be no Assemblies.

CARD ASSEMBLIES

for TWELVE NIGHTS

Will commence as soon as there be FORTY subscribers; the Tickets at 18s each ,Tea included, to be transferable. 
=============================================================== 
So, one paid in advance for a series of tickets. The organisers paid the musicians, catering costs and the hire of the assembly rooms (If such a sum was applicable) from this sum. I note the Newcastle assembly organiser Mr Grieveson was quite astute, and would not proceed until he was assured of making a profit:

“unless there are FORTY subscribers there will be no Assemblies.”