It can be a flat fee or a percentage. I don't do a lot of rental listings, but I did one recently & I just looked around at other comparable rentals in that specific neighborhood to see what other agents were offering & went off of that. I was offering about $600 & our rent price was $2000/mo. The percentage was 2.5% based on the total lease term ($24,000 X 2.5%).
Whew! I'd bring a client for a month's rent (that's over 8% per annum). At least in LA, a majority are posting 3% of the first year's gross rental--which is why no agents focus on leases. You can choose to be typical--or have the favored opinion of many agents bringing clients to you.
Generally the agent gets 2.5-3% of the total lease amount. For example, if you sign a 1 year lease at $2k per month, that is $24k total so the commission paid would be $720 to the agent that brought the buyer.