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.
Airports tend to acquire a lot of land in their vicinity.
This can be to mitigate noise or complaints from people living under approach/departure paths, for safety in the event of insufficient elevation, for future expansion/extensions of runways or of parking facilities for cars/planes etc.
Grazing animals don't tend to worry too much about airplanes, so "spare" land is often used for agriculture and horticulture (growing animals and plants) Low income but low costs too.
Some businesses need to be located near to airports for reasons, like courier/freight operations or rental car pickups. Long-term carparks can be on remote and less-desirable parts of airport land and still generate a profit. All this land can be re-designated as needs change in the future.
Airport companies will also own the roads across their land. This can sometimes lead to odd interpretations and loopholes in road laws. Locally, police cannot ticket a motorist for speeding on airport land roads, because its not public property. So there are an inordinate amount of speedbumps and sharp turns.
Also, bicycles are excluded from some roads used for pickup/drop off.
A motorist pays to use the parking, a traveller pays a departure tax in their ticket, an advertiser pays for billboard or signage space, and a business pays to lease a concession or shop space in the terminal. Ultimately the visitor pays in the form of increased prices, $10 for a coffee.
The airport company controls everything on their land. You cannot get a phone line or fibre installed to your site. Instead, the telco terminates the service in a handover building at the boundary, and the airport company runs the lead-in the rest of the distance. This is a license to print money because there is no competition so they can charge whatever the customer will pay.
Inside the terminal there are strict controls over transmitters too - you can't even have a wireless ethernet network of your own. Instead you have to buy a SSID which is configured on the airport's own wireless infrastructure, and trunked back via a VLAN. Everything costs money every month.
Admittedly this makes sense from a safety standpoint - high power transmitters may have an effect on operations by interfering with aircraft, or more likely interfering with hand-held radios. And the supply of wireless from a single infrastructure will eliminate contention while providing a better and fairer service.
The stinger comes in the setup and on-going costs being a literal monopoly environment.