How do I know when the return and supply halves of my forced hot air
furnace are balanced without a huge expense?I am looking for some
relatively close method and do not care if I am exact.? Is there some
formula for measuring openings of one side versus the other?

I'm not sure exactly what you have in mind when you say you want to
"balance" the return and supply halves of your furnace. In some sense,
the system balances itself automatically. You cannot create or destroy
air mass in your ducts. If the cross-sectional areas are different,
then the flow velocity will adjust so that the mass flow is equal. If
you want the flow velocities to be equal, then you could "balance" the
cross-sectional areas (set them to be equal). More typically, one
simply chooses a return duct (usually a single duct) based on the size
of the blower. The supply duct may start out at the same size, but it
typically branches rapidly to feed individual registers. Every time
the flow splits, the duct size can be reduced if you want the flow
velocity to remain approximately constant. The absolute size of the
duct work can vary within a significant range without grossly changing
the function of the system, but you typically do not want to let the
flow velocity get too high, both because there will tend to be more
noise, and because there will be more frictional loss, pressure drop
and leakage. If you have a number of separate rooms you are trying to
heat from the same furnace, you may need to "balance" the flow
(especially the supply, but possibly also the return) to and from the
separate rooms. This can be done by adjusting the number of supply
registers or throttling the flow of air to existing registers (either
at the register or in the duct). If the rooms are physically isolated,
you made need to consider separate return ducts. Often, natural
openings between rooms are sufficient. Of course, if the relative heat
needs for different rooms varies (say, depending on sun exposure), it
may not be possible to balance the systems for all conditions, and you
may need to create separate heating "zones" (separate furnaces for a
forced air system).

If you are working with a reputable heating contractor, he should be
able to help you sort through these system design issues. If you're
doing the job yourself, there are various resources available to help
you size your components. Typically you choose a furnace and blower
size based on your estimated heat loss and coldest design outside
temperature. That then sets your main supply and return duct sizes.
You can get software packages to help steer you through these
calculations. I can't endorse any particular package, since I haven't
used them, but one that looks easy to use and complete is HVAC-Calc,
available at:

http://hvac-calc.com/index.asp

This package does output some information on duct sizing. For a single
residential user, the price is US$39, and you may even get what you
need from a trial download, if you're not looking for very much
information.

For a little more money, you can also hire someone to do the system
design for you. For example, such a service is provided by Ductworks:

http://www.ductworks.net/html/layout.html

I may be able to provide more specific advice about your particular
system concerns if you provide more information. Are you installing a
new system or adjusting/improving/replacing an existing one? Any
specifications you can provide, both on the heating needs of your
space and any already selected or installed hardware would be helpful.
What specifically are you adding or changing? Feel free to request a
clarification with such information.

Google Search:

forced air furnace duct size calculation
://www.google.com/search?q=forced+air+furnace+duct+size+calculation

terrific!  The answers were exactly what I was looking for and the
suggested web sites will enable me to continue my heating and cooling
projects knowing I am headed in the right direction.  What a great
service.  Got an answer while I slept; it doesn't get any better than
that.