Measure ethanol volume fraction in a beverage
Your question: Given a sample of an alcoholic beverage (be it beer, wine, etc..), what are possible methods to find out the ABV (alcohol by volume) of it with moderate accuracy?


There are a few method used in winery industry as  Karl mentioned a comment in elsewhere. I assume you want to find out better methods to find the alcohol content:


The best technique is the gas chromatography method, which is the most accurate method for determining alcohol content. Gas chromatography has the added benefit of providing additional information about the wine, beer, or any other liquor product (e.g., Ref.1).
Seemingly most popular technique is the determination of ethanol in alcoholic beverages by titrimetric and/or spectrophotometric dichromate methods (e.g., Ref.2-Ref.4).
Another method is enzymatic assay using spectrophotometry: Ethanol, in an alkaline environment, is oxidized through an enzymatic reaction and converted in acetaldehyde in presence of $\mathrm{NAD^+}$, which in turns produces $\mathrm{NADH}$. The increase of the absorbance, measured at $\pu{366 nm}$ (end-point), is proportional to the concentration of ethanol in the sample (e.g., Ref.5).
In addition, you can also use NMR technology to determine the ethanol content in alcoholic beverages (e.g., Ref.6).


References:


M.-L. Wang, Y.-M. Choong, N.-W. Su, and M.-H. Lee, “A rapid method for determination of ethanol in alcoholic beverages using capillary gas chromatography,” Journal of Food and Drug Analysis 2003, 11(2), 133–140.
G. J. Pilone, “Determination of ethanol in wine by titrimetric and spectrophotometric dichromate methods: collaborative study,” J. Assoc. Off. Anal. Chem. 1985, 68(2), 188-190 (https://www.ncbi.nlm.nih.gov/pubmed/3988696).
Arthur Caputi, Masao Ueda, Thomas Brown, "Spectrophotometric Determination of Ethanol in Wine," Am. J. Enol. Vitic. 1968, 19(3), 160-165 (https://www.ajevonline.org/content/19/3/160).
Malinee Sriariyanun, Parita Mutrakulcharoen, Surapun Tepaamorndech, Kraipat Cheenkachorn, Kittipong Rattanaporn, "A Rapid Spectrophotometric Method for Quantitative Determination of Ethanol in Fermentation Products," Oriental Journal of Chemistry  2019, 35(2), 744-750 (http://dx.doi.org/10.13005/ojc/350234).
Amy A. Caudy, "Spectrophotometric Analysis of Ethanol and Glucose Concentrations in Yeast Culture Media," Cold Spring Harbor Protocol  2017, (9), 735-741 (doi: 10.1101/pdb.prot089102).
Meden F. Isaac-Lam, Thomas Brown, "Determination of Alcohol Content in Alcoholic Beverages Using 45 MHz Benchtop NMR Spectrometer," International Journal of Spectroscopy 2016,  Article ID 2526946, 8 pages (https://doi.org/10.1155/2016/2526946).