There are several methods of measuring the alcohol content (%abv = alcohol by volume) of a liquid, all require a representative, homogenous sample.
The principal methods are:-

Density and Refractive Index method:
The refractive index of alcohol is different from water, so can be used as an indicator of alcohol content. It is the quickest method, taking only a few minutes. It is prone to interference by other compounds in the wine, but the accuracy is dependent mainly on correcting for the temperature of the wine, a sophisticated refractometer will have a temperature compensation facility, the accuracy can be at best +-0.5% abv.

Distillation followed by hydrometry/refractometry method:
The alcohol must first be separated from the wine by distillation with suitable equipment. The specific gravity of the distilled alcohol is then determined with a hydrometer which is calibrated directly in %abv at 20 °C. If the distillate temperature varies from 20 °C then a correction needs to be applied, since the volume of the liquid changes with temperature. 0.1 %abv is added for each 0.5 °C below 20 °C, or subtracted for each 0.5 °C above 20 °C, so this is very significant.
This is a complex and time consuming procedure, the accuracy can be affected by the work of the technician as there are various possible causes of error, such as interference from co-distilled compounds, when there are ethyl esters (cleaved to ethanol during the analysis) and other alkali-stable steam volatile compounds present.

A much more expensive but superior alternative to the hydrometer: The MISCO Palm Abbe VINO5 Digital Wine-Alcohol Refractometer from USA (www.misco.com) is engineered specifically for testing the potential alcohol content of grape must, and the actual %abv in the finished wine.
Measurements are made with precision comparable to mid-range bench-top refractometers costing thousands of dollars more.
The actual %abv of a particular finished wine can be established following procedures and methods recognized by international bodies.
After distilling a small volume of wine, the ethanol distillate is measured on the Palm Abbe VINO5 Digital Wine/Alcohol Refractometer and the actual alcoholic strength (%abv) or specific gravity is displayed. Protection against inaccurate readings due to temperature differences (a major concern in refractive index measurement) is assured with non-linear temperature compensation specific to grape juices. Temperature compensation is automatic for fluids read between 0 and 50 °C. The accuracy is claimed to be +-0.25 %abv, twice the accuracy of competing instruments.

Ebulliometer method:
The ebulliometer is a measuring device that is designed to evaluate the boiling point of different types of liquids. It's use in the wine industry is based on the fact that alcohol boils at 78.4 °C, a lower temperature than water, so the boiling point of alcohol-water mixtures changes as a function of their concentration. A precision thermometer is involved, to determine the boiling temperature of the wine within 0.02 °C. The boiling point of any liquid depends on the atmospheric pressure, so the zero point has to be set against the boiling point of pure water prior to starting each test.
The method is fairly quick and sufficiently accurate (+-0.5 %abv) for general purposes.
It is affected by atmospheric pressure changes, a barometric change of 4 mm (during a test) would cause an error of 0.5 %abv. A simple ebulliometer is less accurate than the Distillation method.

There are two modern types of the device that are currently in use. The Swietoslawski ebulliometer relies on an isobaric method.
This form of ebulliometer contains a boiler, Cotterell pumps, a condenser, and a thermowell.
The measurements obtained with this type of ebulliometer are considered to be very exact. An isobaric ebulliometer provides measurements of such factors as the exact temperature needed to reach a boiling point, solvent purities within the properties of the wine sample, and the molecular weight of the substance. The use of a resistance temperature device helps to create the accurate readings on the vapor-liquid equilibrium of the wine, which is one factor that makes the isobaric approach the most accurate reading possible with this type of device.
An isothermal ebulliometer contains similar components as the isobaric type, but usually involves the presence of a stirring mechanism that is operated by a small pump. The stirring takes place during the process of boiling the mixture and is thought to increase the chances for a more accurate reading of such gases within the mixture as methanol. While not as prominently in use as the isobaric type, there are a some wineries that prefer this method.

Gas chromatography (GC) method:
The equipment is expensive to buy so the analysis is normally carried out by contract analytical chemists. It is considered to be the most accurate means of ascertaining the alcohol content of wines and is used by HM Customs & Excise.

Essentially, the gas chromatograph works by analyzing the mixture of organic compounds found in the wine. The gas chromatograph has a series of filters made from porous materials. Samples taken from the wine batch are gathered into a syringe and then injected into an ejector port on the device. The temperature of the injector port must be in excess of the boiling point for the sample in order accurate readings to occur. This allows the components of the wine to convert into gas, which then is then pushed into the filters by way of helium or a similar carrier gas.
As the wine gases pass through the filters, the compounds are identified by electronic equipment and the alcohol content is determined. While some models of the gas chromatograph feature a printer that creates a graph of the progress of the wine sample, new models utilize a terminal display, making it possible to view the results without having to decipher a graph.

Modern gas chromatographs are smaller and less expensive to purchase and maintain compared to equipment from years ago. Using a gas chromatograph for alcohol measurement has the extra benefit of providing the winemaker with additional information on the nature of the wine.
There are a number of manufacturers around the world that provide state of the art gas chromatograph equipment to the wine industry. Research and development departments at these manufacturers routinely find ways to fine tune the efficiency of their products, which makes it possible for the process of accurately gauging the alcohol content of wine more accurate every year.

Spectroscopy (infra red) method:
The Alcolyzer Wine from Anton Paar which uses a patented method based on Near Infrared spectroscopy to determine the alcohol content in a highly alcohol-specific range. For this reason, the other constituents of the beverage do not influence the result. This means, the determination of white or red wine, sweet or dry wine, can all be done with one adjustment.
A highly alcohol-specific range of the spectrum was identified between 1150 and 1200 nm. The evaluation method uses the significant alcohol peak in this area and two spectral points very close to it for defining the baseline. Extensive investigations showed that the alcohol results based on this type of evaluation are virtually free of influences from other known wine constituents. This allows adjustments to be done simply with water for the zero point and one binary ethanol/water mixture.The Alcolyzer Wine utilizes an optical set-up without any moving parts. The instrument consists of a Near Infrared Light Emitting Diode, a condenser lens, a sample cell, a collimator lens to focus the parallel beam and a grating spectrometer with a detector array. The absorption information read by the detector array is used to determine the alcohol content of the sample. A measurement is carried out in less than one minute. The Alcolyzer Wine has a built-in Peltier thermostat to ensure accurate and automatic control of the temperature in best time. Consequently, there is no need for manual temperature adjustment and correction.

Methods such as the combined density and refractive index method or Ebulliometer determination tend to be inaccurate because the underlying measuring properties are non-specific to alcohol. Traditional analysis methods such as distillation are time consuming and require experienced operators. The accuracy of the above mentioned methods can be difficult to maintain and repeatability is often at unacceptable levels. Compared to distillation, an acknowledged reference method for alcohol determination, the Alcolyzer Wine achieves accuracies of ± 0.1 %abv and repeatabilities of ± 0.01 %abv.

More recently a Mid Infrared wine analyzer has been released that has similar accuracies to the Anton Parr Near Infrared instrument with a cheaper price.  If you want information about it contact: Spectro Scientific.

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