HVAC stands for "Heating, Venting, and Air Conditioning".  In other words, it's a system that provides heating and cooling.

Sizing an HVAC simply means figuring out what size system is needed to cool or heat your home properly.  Sizing is important because a unit that's too small won't cool your house well, and a unit that's too big will cost more than necessary (as well as other possible problems).  Most contractors will try to sell you a system that's too big, either because they're trying to make more money, or because they don't know how to properly do the sizing work. (sources 1, 2, 3, 4)

So, the best way to size your system is to have a "Manual J" calculation done on your house.  That's the gold standard for system sizing, taking into account things like how much insulation you have, what kind of windows and what direction they're facing, and everything else.  Many utility companies will do this for free (check with them), and if not, you can hire an energy auditor.  Do not go with an HVAC contractor for the Manual J (which has an obvious conflict of interest in wanting to sell you a bigger system than you need), go with your utility or an energy auditor so you can trust that they did it right.  They'll tell you exactly what size you need, and you can shop accordingly.

You should also have the efficiency of your ducts tested, because installing properly-sized equipment won't do any good if you're going to gain or lose lots of BTUs through your ductwork.  The national average performance of ducts is only 57%. (source)  If your ducts are a problem, then have them serviced.  Of course, if your ducts are running through conditioned space, then duct losses are not a problem, because you "lose" the air right into the area that you were trying to condition in the first place.

The problems with oversized systems is that they cost more, which is just wasted money, and they're often not as comfortable.  (They might blast you with too-hot air in the winter, and they cause uneven temperatures throughout the house, because they don't run as much, so the air isn't circulated as much as it would be with a right-sized system.)  Conventional wisdom is that oversizing also creates other problems besides cost and less comfort, but I consider those to be mostly myths.

1. MYTH: Oversized AC's don't control humidity as well.  The theory here is that oversized systems don't run long enough to dry the air.  This is only sometimes true.  A university study of homes where grossly oversized units were replaced with right-sized units didn't result in lower humidity.  The researchers theorized that the longer running time of the right-sized units meant that the fans they were drawing in more moisture into the house through the building envelope and the attic. (source PDF)  And Martin Holladay, an icon in the building science field, says, "Oversized air conditioners aren't really as terrible at dehumidification as many energy experts claim." (source)  However, I know of at least one case in which an oversized system reportedly resulted in more humidity.
   
   
2. MYTH: Oversized systems wear out faster because of short-cycling.  The theory here is that big systems heat or cool the house so quickly that they shut off after just a few minutes, and the constant on/off cycling is hard on the equipment.  There are a few problems with that:  First, it's hard to believe that the extra cycles would really make a big difference in equipment life.  The AC will likely be up for replacement just because it's old before it dies completely.  Second, any stress added by extra cycles should be balanced by the fact that the equipment doesn't run as long.  Finally, most modern equipment runs at various speeds (ramping up or down to adjust to the heating or cooling load).  So, when they need to run just a little bit, they dial themselves down automatically.
   
   
3. MYTH: Oversized systems use extra energy.  The theory is that AC's need to run for several minutes to get efficient.  But the study above found that they don't use more energy overall.  However, for mini-split systems, especially heaters, oversized systems can use a lot more energy. (source)

Heat is measured in BTU's (British Thermal Units).  For example, a heater might supply 24,000 BTUs per hour to a house when it's operating.  To size a heating system, we figure how many BTUs of heat the house loses to the outside, and then get a system big enough to replace the BTUs that were lost.

We use BTUs for cooling, too, to measure how much heat an air conditioner removes from a house or a room.  For example, a small window-unit AC will remove about 5000 BTU per hour from a room.  When we size for cooling, we'll be figuring out how many BTUs of heat enter the house, and then get a system that can remove that much heat.

AC equipment is also measured in tons.  This has nothing to do with the weight of the equipment, it's just a measurement of heat.  One ton is 12,000 BTU.  So a 2.5-ton system would be 2.5 tons x 12,000 BTU/ton = 30,000 BTU.

Here's a problem you might have:  You've hired out the Manual J calculation and it's come back at 27k BTU for cooling and 53k BTU for heating.  But the contractors don't have 27k BTU air conditioners, they've got 24k and 30k, and they don't have the exact size furnace you need, either.  Do you go with the next size bigger or the next size smaller?

You generally go the next size bigger.  Going slightly bigger won't be a big price penalty, and it'll ensure that the system can handle the load on extreme temperature days.  If you go smaller, even a little smaller, you might be a little uncomfortable on the coldest and hottest days of the year.

The Manual S limit is to not go beyond 15% more BTUs than you need for cooling (25% for heat pumps), and not more than 40% more BTUs than you need for heating. (source)

Just like "Manual J" is used to figure the heating & cooling load, "Manual S" is used to select the equipment to handle the load.   The reason for this is that the actual BTUs delivered or removed by the unit might not match the rating of the unit depending on things such as temperature and humidity in your area.  However, matching your calculated BTUs from Manual J with the nameplate BTU rating on the equipment is probably sufficient for most situations.

The worst way to size a system is by square feet, though many contractors do just that.  The first problem is that it doesn't take into account the climate (hot or cold), how much insulation you have, whether the house is shaded, how leaky the house is, etc.  The other problem is that it estimates only cooling; there's no rule of thumb for heating based on only square feet, because such an estimate would often be even farther off.

But for what it's worth, which is not much, the basic formula for cooling is 1 ton of cooling for every 600 s.f. of house.  So, for example, a 2400 s.f. home would need 2400 s.f. x 1 ton/600 s.f. = 4 tons.  Newer homes that are insulated well and aren't leaky would be closer to around 1 ton for every 1000 s.f.  You could invert the figures if that's more comfortable.  Another way of saying 1 ton for every 600 s.f., is 20 BTU per square foot.  Another way of saying 1 ton per 1000 s.f. is 12 BTU per square foot.

HVAC System Sizing
	Blue	Green	Yellow	Orange	Red
Cooling
1.5 tons	700-1100 sf	700-1050 sf	600-1000 sf	600-950 sf	600-900 sf
2 tons	1101-1400 sf	1051-1350 sf	1001-1300 sf	951-1250 sf	901-1200 sf
2.5 tons	1401-1650 sf	1351-1600 sf	1301-1600 sf	1251-1550 sf	1201-1500 sf
3 tons	1651-2100 sf	1601-2000 sf	1601-1900 sf	1501-1850 sf	1501-1800 sf
3.5 tons	2101-2300 sf	2001-2250 sf	1901-2200 sf	1851-2150 sf	1801-2100 sf
4 tons	2301-2700 sf	2251-2700 sf	2201-2600 sf	2151-2500 sf	2101-2400 sf
5 tons	2701-3300 sf	2751-3300 sf	2601-3200 sf	2501-3100 sf	2401-3000 sf
Heating
	40-60 BTU/sf	35-50 BTU/sf	30-45 BTU/sf	20-40 BTU/sf	15-35 BTU/sf
Map from DoE.  Data from AC Direct with permission, with my modifications for heat.

By taking climate into account, you can estimate heating as well.  While some people will estimate cooling based on square feet alone even though it's not accurate, nobody will estimate heating by square foot alone, because the results can be even farther off.  At a minimum, heating estimates must take into account the climate as well as the area to be heated.  (A study of office buildings showed that a building in Chicago needed three times less cooling than one in Miami, but it needed 48 times more heating. (source))

You can see the estimates in the table at right.  To make this method a little less useless, I give it with ranges rather than a static number.  You'll need more powerful equipment if you don't have good insulation and windows, less if you do.

There are various calculators on the net that try to help you size your system, but I didn't like any of them enough to recommend them.  I'd like to build my own to offer to my readers, but I've been having a hard time finding the data to use for the calculations.  (Manual J is too big for this project; what I'm envisioning is more like a "Mini-Manual J".)  Any readers who have data to share are welcome to contact me.  Mostly, I need the formulas.  I can look up things like heating/cooling degree days, and U-values and R-values for various building materials, it's the formulas to assemble those into an answer that I lack.  I'd like to account for losses/gains from ceilings, walls, windows, doors, floors, occupants, electrical devices, ductwork, leakiness, and shading.

A "Manual J" calculation is the gold standard for sizing HVAC equipment.  It's not something a homeowner can do themselves (unless they're willing to throw down $500 for the software, and confident that they can use it accurately).  Many utility companies will do the calculation for you, and failing that, you can hire an energy auditor.  Don't rely on an HVAC contractor to do your Manual J, since contractors frequently churn out bad Manual J's by using the wrong inputs—either because they're trying to upsell bigger equipment, or because they sincerely don't know how to use the software properly.