How do airports generate "indirect" income i.e. income from things other than aviation operations (landing, FBO services, repairs)?
One way to approach this question is to look at the annual budget for an airport. I'm going to assume that you mean a large passenger airport as opposed to one focused on serving general aviation, cargo, etc...
Let's use SFO (San Francisco International) as our example. It's a city-owned airport, so the budget is a public document. Here's the budget for FY2014/15 and FY2015/16.
Page 5 (page 7 in the PDF) breaks down major sources of revenue. We have some that fall into the category of "direct" revenue in your question: landing fees, terminal rentals, etc... under the "aviation" category. Some of the terminal rental fees include space for purposes you might not consider aviation uses, like back offices for airline staff We also have $60-80M in "PFC Revenue." PFC stands for "Passenger Facility Charge"; it's a charge that is added to the ticket price of everyone flying out of that airport.
Finally, there are the non-aviation revenues. The bulk of those come in two categories: parking and concessions. Parking is self-explanatory. Concessions describes all the independent businesses that operate at the airport. Many businesses lease terminal space for retail shops (including duty-free), restaurants and take-out food, lounges, currency exchange, etc... They all pay rent and/or a share of revenue to the airport based on the terms of their lease. SFO also books about $23M/year in revenue off the sale of electricity, as the airport sells electricity to its tenants (airlines, concessions, etc...). I suspect, but am not positive, that these electricity sales are a nice moneymaker for the airport, as it can purchase hydropower from the City at extremely low cost and resell it at market (utility company) rates to its tenants. This is a quirk particular to San Francisco however.
If you scroll through the detailed budget in the PDF, you'll find entries for other revenue categories. Examples include advertising fees (Clear Channel pays the airport to put up ads in the terminals and other areas), revenue for things like ATMs and baggage carts, leases to rental car companies, fees paid by taxicabs and airport buses for the right to access airport property, and even permit fees paid by filmmakers and photographers using the airport. Heck, the airport even charges the regional transit agency $3.2M/year in rent and custodial fees for the airport train station. Browsing through the budget should give you a pretty good idea where a large US airport can make money from non-aviation services.