Soil should first be processed by drying the soil to ensure a standard "dry" sample is analyzed. 55$^o$C in drying ovens for 24 hours works for most non-water-zone soils, but more time at 50 - 55 $^o$C (as long as it's consistent between samples) can be used to dry out wetter samples. One can then put the soil through sieves to remove rocks and other debris (2mm sieve is common).
To actually measure soil pH, one combines 1 part soil with 1 part water and then measure with an electrode (McLean 1982)$^1$.
By always using 1 part soil to 1 part water, you maintain a consistent relative amount of water per sample and therefore can account for different sample sizes.
The final value is reported as pH.
You can find the McLean (1982) resource here for $15 or likely for free from a nearby university library. The paper has been cited over 2800 times.
 McLean, E.O. 1982. Soil pH and lime requirement. In A.L. Page et al. (ed.) Methods of soil analysis, part 2. Agronomy Monogr. 9, 2nd ed. ASA and SSSA pp 199–223.
As @Roland pointed out in the comments, other standards do exist.
For example, the International Organization for Standardization (ISO) maintains reports describing standard protocols for different methods (which therefore are sometimes used):
ISO 10390:2005 specifies an instrumental method for the routine determination of pH using a glass electrode in a 1:5 (volume fraction) suspension of soil in water (pH in H2O), in 1 mol/l potassium chloride solution (pH in KCl) or in 0,01 mol/l calcium chloride solution (pH in CaCl2).
ISO 10390:2005 is applicable to all types of air-dried soil samples, for example pretreated in accordance with ISO 11464.
The USDA describes several standard protocols used by their laboratory at the National Soil Survey Center to measure soil pH (Hydrogen-Ion Activity) in their Soil Survey Laboratory Methods Manual (version 5, 2014). See specifically, pages 265-281 for various soil suspension and soil extract methods.
The EPA (US Environmental Protection Agency) similarly has a protocol that they use. Their electrometric approach using a digital pH meter involves the insertion of a glass electrode into a soil suspension made by mixing the soil 1:1 with a reagent solution (see referenced notes below).
Again, the overall takeaways are:
- Reporting soil acidity as pH is standard
- There are multiple standard methods to measure the pH; Just be sure to properly cite your approach!