Beans, Bullets, Bandages, Fuel, Parts, Replacements. Our Army military logistic system is well known, and anyone with internet access can learn about it. Here is an introduction for those who may not be familiar.
The military supply system lays out classes of supply 1 through 10.
Class 1: Food and Water
Class 2: Office Supplies and such
Class 3: Fuel, lubricants, and other petroleum products
Class 4: Building materials
Class 5: Ammunition
Class 6: Comfort and convenience items
Class 7: Major end items
Class 8: Medical Supplies
Class 9: Repair Parts
Class 10: The "catch all" category, usually for things like seeds or fertilizer for civil affairs.
The "Loggies" (slang for logistician) are the best resource trackers and predictors a Commander has on his staff. In addition to tracking all the classes of supply by stocks on hand and predicting stocks for the future, they also have to plan on moving it all from "point A to point B" and distributing it out.
The Loggies are the strategic reason that insurgents don't bother attacking Combat Logistic Patrols (CLP, or "clip") very often. Not because it wouldn't have an effect, but because a CLP is designed to "plus up" a unit instead of "resupply" a unit. If a unit is cut off from a CLP for a bit they don't go black immediately, and due to the power of forecasting the Loggies know exactly how to shift priorities of effort to keep the boots on the ground in the fight.
John Mosby has written quite a bit about insurgent logistics (part two here). I'm going to look at this from the perspective that I know about, which is operations to find and clear insurgent caches. Mostly finding a cache is a not the purpose of an operation, usually you are going after some other target. However, sometimes patrols really are sent out just to do clearance operations and look for caches. In Afghanistan "cache" universally means "weapons and ammunition" as the remaining classes of supply for the insurgents are "off the economy" so to speak.
First, you need to know about something called a Company Operations Intelligence Support Team (COIST). The Army has a decent article here http://www.army.mil/article/23048/coist-staffs-play-crucial-role-on-todays-complex-battlefield/ that outlines the duties of COIST members, and the capabilities that they bring to the fight.
Remember that "Sustainment" is an element of Combat Power (the 6 War Fighting Functions plus Leadership). Traditionally one of the ways to defeat an enemy was to "starve them out." You can attack any portion of the Elements of Combat Power, and here we will look at insurgent sustainment.
First, where are the insurgents operating? Get a map, use pushpins or alcohol pens to outline where the enemy is operating. This is his AO. A good cache point is accessible for resupply, so focus your operations in and around the enemy AO. You can use computer tools such as Google Earth or any other commercial mapping software to do this, and electronic products are usually easier to share with others.
Second, what is the enemy using? Small arms ammunition is a lot easier to conceal than 152mm artillery shells used to make IEDs. Know what the enemy is using from After Action Reports and Patrol Debriefs to add specificity to your search for enemy caches.
Third, are there any suspicious areas of inactivity? People don't like to fight where they live if they can avoid it. If the only difference between area A and area B is the level of conflict, it bears looking into. This is where the military intelligence guys can come in handy, finding out what the scuttlebutt is on why neighborhood A is quiet.
Fourth, where are the natural supply lines in and out of the AO? This is a natural place to look for caches. People are lazy and don't want to haul stuff any further than they have to before using it.
Fifth, is there any unexplainable or "fishy" activity in the AO? I know several officers who noticed something out of place which led to a cache find. A field being plowed in winter, a grain sack with a bulge in it, a wooden floor in a home (a bit of a rarity where we are fighting). If something doesn't feel right, stop, ask yourself what is triggering that feeling, then investigate.
These are all examples of questions that a good COIST will be asking and trying to answer. A COIST isn't there to act as a company level S2, but as an intel focused battle tracker and trend analyzer. We know that we won't win the fight by taking out caches, but we know that we can't provide security if the enemy can resupply at will.