Here I will go into detail of what I know about hub-centric wheels, a little bit about lug-centric wheels, and finding wheels for your vehicle.

Parts of a wheel: Tire, rim, spokes, hub, hub ring, lug nuts/bolts, hub cap/center cap, wheel wieghts, valve, valve cap,.
Wheel tech. terms: Mounting, balancing, PCD (Pitch Circle Diameter), diameter, width, tread depth, tread wear, centerbore, bolt pattern, asspect ratio/series, arch, wheel well, flare, bias ply, radial, bead.

Premise: Wheels are supposedly circular and provide smooth and continous contact with the road.

For this premise to hold true, the center of rotation of each wheel should line up with the center of rotation of the respective axles and hubs. If this is not done in a satisfactory manner, vibrations will result and will get progressively more pronouced as speed increases.

The purpose of blancing wheels is to locate the center of rotation by mass to be in the same place as the geometric center dictated by the lug holes.

Lug-centric wheels:
Lug-centric wheels use the lug nuts or bolts to center the wheel on the hub. Apparently it is quite an antiquated system and not as effective as hub-centric centerring. From here on it should be assumed that I refer to hub-centric wheels.

Hub-centric wheels:
The bored out center of a hub-centric wheel fits closely around a proturding ring, known as a flange, from the face of the hub, and thus centers the wheel on the hub.

Majority of the wheels today are hub-centric, and leave it to auto manufacturers not to have a standard size for centerring. Thusly, wheels manufactured by auto manufacturers probably won't fit the hubs of other auto manufacturers. It isn't impossible to make the fit happen, it just takes more work and will probably involve machining.

After market wheel manufacturers have the problem of making wheels that fit many vehicles. Each fit is called an "application". There are a couple of ways to achieve fit for their manufactured wheels.

One method is to machine wheels for each specific application. In this way every wheel purchased will fit at least one, maybe a certain set of cars, and perhaps only certain hubs (front or back) of those cars. The benefit of this method is that a fit is guaranteed without additional hardware to worry about. The drawback is that the manufacturer must either carry a large inventory or machine center bore diameters on demand, or somewhere in between. The drawback for the consumer is that the wheels can only be sold to owners of same or smaller application cars.
The other method is to machine the center bore of every wheel to a larger size than most or all available hub flange diameters. Then it is up to the dealer or consumer to fit a space filler, known as a hub ring to the wheel to allow hub-centric centerring. The benefit of this method is that a uniform and hopefully smaller inventory can be held. The drawback is that additional hardware must be found, obtained, and installed for proper wheel installation.
"Plus sizing"
"Plus sizing", as opposed to, "getting bigger wheels". Not one of the better technical term replacements, but I guess it goes with the various methods of achieving larger wheels.

Firstly, caculating wheel size. I will be using the common P-metric and Euro metric system for sizing. For those who do not intend to install a new speedometer or recalibrate their current one, it is important to retain a tire diameter as close to stock as possible. As an aside, in Ontario it is illegal to have a speedomter that indicates slower than actual speed.

For my car (2004 Toyota Echo hatchback), the stock tire size was 175/65R14. The diameter works out to be the following, 175mm x .65 x 2 / (25.4mm/inch) + 14in. = 22.96in. Even with these numbers and calculations the diameter is still rough. I surmise the reason for this is to keep buying and selling tires somewhat simple.
Some tire manufacturers offer many numbers that characterize their tires. They'll more than likely have the P-metric/Euro metric numbers. However, if available the revolutions per mile or kilometer is very interesting, for it potentially offers a very accurate measurement of tire diameter. How is this possible, one may ask? Well, remember from elementary/middle school math where a circle diameter is equal to the circumference divided by PI(3.14159...). Thusly to calculate the diameter using revolustions per mile/km, take mile or km divide by revolutions then divide by PI. Make sure the units work out properly. My Michelin tire does not list the revolutions per mile/km.

Rim numbers
The numbers on rims look like, "14x5.5et40JJ". This is once again from my stock rims. It means that my rims are 14" diameter, 5.5" width, positive offset of 40mm, and a lip shape of JJ.

Lug nuts
The lug nuts that come stock on my vihicle are 21mm, hex socket, M12x1.5, 60 degree taper/cone face nuts. This means to install the lugs requires a 21mm socket & wrench, which comes with the car. The lugs fit on [posts] that are 12mm in diameter, and have a thread pitch of 1.5mm (fine). The contact surface of the lugs for the rim are of the taper/cone type angled at 60 degrees.
Researching what wheels are safe or designed for your car

Now that we have the nominal tire diameter for the car we can proceed to chose a larger wheel to install. Let's increase the wheel diameter by one inch to a mighty 15 inches.

Purely by the numbers I could go get a set of 21"... a heck! 22" wheels and install them on my car. The bigger the better! ;) I can do this because the wheels are still smaller than the tire diameter, right? This, to the woe of some car tuners, does not work for a number of reasons. Primarily the tire limits the maximum diameter of the wheel. More sepecifically the tire supply and demand, and a chunck of physical reality.