Science to the rescue!
3M makes a type of insulating window film similar to saran wrap but thicker and designed to be applied with a hair dryer so it shrinks to be perfectly clear around your window frames.
At about $15 for 5 windows, it fits your cost parameters too.
lifehacks.stackexchange.com/users/1495/Digital Chris
Home-made pelmets Heavy curtains are a good start if you can afford them, but if you already have curtains or blinds of any kind, adding pelmets will make a significant difference.
Pelmets reduce convection currents, whereby air coming into contact with the window surface cools down, falls to the floor and pulls more warm air down past the top of the curtain, ad infinitum.
With such a tight budget, making your own pelmets is probably the best option.
Google "home-made pelmets" for some instructions.
(You could also try "box valance" instead of pelmet.)
Here are a couple of examples: http://www.instructables.com/id/How-to-save-heat-money-and-energy-with-easy-pelm/ http://www.thecreativityexchange.com/2012/11/how-to-diy-a-pelmet-or-box-valance.html
lifehacks.stackexchange.com/users/10325/Igby Largeman
The old standby for this was "temporary storm windows", for houses that lacked custom-fitted storm windows.
A storm window overlays the window frame on the outside to prevent exterior air (along with rain, snow, etc.)
from directly contacting the single-pane sashes; it provides some insulation (less effective than modern multipane glass, but much better than nothing), as well as physical protection (storm windows were often shatterproof acrylic plastic).
Temporary storm windows are a simple clear plastic sheet (plastic drop cloth, plastic tarp, etc., as long as it's clear), held in place by a strip of lath on each edge, which is stapled or brad nailed to the window frame.
The clear plastic provides an airflow seal, some trapped air insulation, and physical protection (less so than acrylic sheet, but still much better than nothing), and is very inexpensive: they used to sell kits in hardware stores, but you can buy clear plastic sheet, lath, and brads cheaply at the big box home improvement stored.
These are disposable; removing them in the spring destroys at least the plastic.
They're cheap enough, however, that that isn't a big deal compared to the heating fuel savings.
Long term, you're best off if you can afford to have the windows replaced with proper multipane glass -- but temporary storm windows are a good, cheap, short term solution that worked well for many years before the current solution was available.
lifehacks.stackexchange.com/users/9830/Zeiss Ikon
I've successfully used pieces of bubble wrap trimmed to fit the glass, with no gaps at the side.
You can wet the smooth side of the bubble wrap with soap/detergent and water, and simply stick it to the glass.
Light transmission is a little reduced, but the view is obscured significantly.
The cost is probably $0, and you can layer this solution with curtains and other suggestions.
lifehacks.stackexchange.com/users/10670/Criggie
I've seen my grandmother put saran wrap on the windows of her old lakeside house in the winter.
When I traveled in New Zealand where most of the houses seemed poorly insulated, I saw a lot of people put saran wrap on their windows for the winter.
Basically, they would stick the saran wrap directly to the glass in order to cover its entire surface.
lifehacks.stackexchange.com/users/10663/le petit prince
One really effective way is to add a new pane to the windows.
This can be done as a temporary storm window as suggested by Zeiss Ikon on the outside, or it can be done on the inside.
If done on the inside it doesn't demand that much work securing the new pane as the weather doesn't have access to it.
This also means you can use simpler arrangement for attaching the extra pane.
So my suggestion would be to buy acrylic glass/plexiglass (4mm?), which can be bought at reasonable prices, and simply use a saw to fit them to the inner frame of your window.
This extra layer between the real window and the extra pane will give you some extra insulation.
And if done properly, you can easily reuse the panes the following year.
Depending on your handyman skills, you could also attach a simple frame for easier handling.
lifehacks.stackexchange.com/users/4490/holroy
"Curtains" is too short an answer
so I added these extra words.
(some curtains are very light fabric that allows some light).
lifehacks.stackexchange.com/users/9683/ssaltman
Put weather stripping on moving parts, and then apply a special plastic film over the window area, trapping a layer of air between it and the window.
Check out " How to Weatherize Windows with Plastic Film Insulation" from Green Dream , for a simple demo of how to do this cheaply.
lifehacks.stackexchange.com/users/7257/WBT
As winter approaches in the Northern hemisphere, one can feel the cold air near interior windows.   How can I reduce the amount of heat lost through windows?  Essential criteria:   cost must be less than $100 for multiple windows  must not block all light  must be either removable and non-damaging or allow for opening of windows come spring   Related:  Seal a window Temporarily (in monsoons)
What is a cost effective way to eliminate heat loss through windows?
lifehacks.stackexchange.com
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lifehacks.stackexchange.com/questions/10001
lifehacks.stackexchange.com/users/2431/Minnow
There are a few different ways of preventing heat loss through windows, and one traditionally way was to install "temporary storm windows" which are a simple clear plastic sheet, held in place by a strip of lath on each edge. You could also consider installing another pane of glass. Other feasible solutions include sticking bubble wrap or saran wrap to the inside of the windows. The options are to attach additional plexiglass panes inside or outside the existing windows or to cut out sheets of bubble wrap or other film to stick to the windows.
Attach an additional external or internal plexiglass window to all your windows. Cut out bubble wrap sheets and attach to the windows. Stick saran wrap or other film to the windows.