I know this stuff! Really. The answer depends on the geometry of your attic and the level of improvement depends largely on the rest of your home. If you are gaining lots of heat through the roof then it might help. If you have a newer house, and have R19 batting or blown insulation in your attic, then you would be unlikely to notice a difference. Scraps of foils blown loosely on top of batting would be bad, and would be unlikely to do anything constructive due to a phenomonon called cavity absorbtivity.
Heres the deal: A bunch of heat in the form of sunlight is absorbed by your roof. The roof gets hot and some of this heat is transfered by the roof radiating heat in the infrared spectrum to the top of the insulation above your ceiling. All the radiant barrier does is to decrease the emissivity of the attic side of your roof, or in the case of something you would place on top of your ceiling insulation, it would decrease the amount of IR radiation absorbed. The question is how much is the heat gain being decreased? Lots of the roofs heat is probably being transfered convectively, by air in the attic getting hot heating the ceiling. Heat moves conductively through the rafters as well, but probably not a whole lot. If you don’t have many rafters, and the attic is well ventilated either through sofit vents or with a powered attic fan, then the radiant barrier might be somewhat effective.
Do a test. On a day when it is hot outside, in the late afternoon touch the ceiling inside and see if it is hot. If it is then you are getting some significant heat gain through it. If it isn’t, then a radiant barrier probably won’t do much.
Personally, I think radiant barriers are overrated. Once they get dusty, which anything in an attic will, then they will lose their effectiveness. Get a big tree to block the sun from hitting the roof and the rest of the house. If you get one that is leafy in the summer but bare in the winter than you won’t increase your heating bill.
If I was spending the money I would go with a powered attic ventilator and/or additional insulation first. That and sealing / caulking / weatherstripping the windows, doors, attic access hole, switchplates, ceiling light fixtures and smoke detectors. Also change or clean your filters regularly, and check out your ducts and make sure they aren’t leaking. If they are don’t fix them with duct tape! Use real serious foil tape for ducts and put it on right. Then check out your return-air plenum and seal any joints in it that lead to the attic, exterior or an interior wall space. Builders don’t do this because the A/C guy says it’s the framers job, and the framer says it’s the A/C guys job. Sometimes plenums have huge holes dirrectly leading into the attic or outside, and they pull hot dirty air in from there which sends A/C bills throught the roof. It is insane, but it even happens in new houses. That and people cut holes to run wires or cable, and then don’t seal them up right.
Also remember than any air that leaves the house will be replaced by outside air. The bathroom fans should be used to get rid of humid air during and after a shower, but if someone is stinky then light a candle for a little while. Also don’t leave regular fans on when they aren’t blowing on anyone. They add heat to the space and make it warmer. I have heard of people trying to use ceiling fans in a closed up house, and not understanding why they get warmer.