how does insurance agents and brokers get paid after writng policies?

It probably depends somewhat on the specific agent and employer.

fwiw, I got paid by the underwriting company directly, about 2 weeks
after submitting the policy.  Different states may have different
cancellation windows that affect this time period.  Commission is a
percentage of the first year's premium.  The insurance company pays
the broker, he takes his cut, and then the rest goes to the agent. 
The ins company will charge the money back to the agent if the client
cancels in the first year, or whatever time frame they set.  Some
policies do pay a residual commision to the agent after the 1st year,
but it is usually a *very* small percentage compared to the initial
sales commission.  For some agents with many clients, residuals can
add up, but insurance sales is a high turnover occupation.  Most
agents do not last long enough to see residual checks.

Are you seeking information specific to P&C or L&H.  The above answer
seems specific to L&H.  Are you asking about commission percentages,
salary of captives, etc?  What exactly are you looking for?  Your
question is very broad.

I forgot to mention I sold life insurance only, my fault.