You can find the answer within the M&M in the following article:
El-Juhany, L. I.; I. M. Aref and A. I. M. Ahmed (2008). Response of Eucalyptus camaldulensis, Eucalyptus microtheca and Eucalyptus intertexta seedlings to irrigation with saline water. World Journal of Agricultural Sciences 4(S): 825-834.
A known weight of oven-dried leaves was digested in concentrated HNO3 then filtration was carried out and filtrate was made up to known volume with distilled water. Flame spectrophotometry was used for determining Na+ and K+, while Ca2+ and Mg2+ were measured by atomic absorption spectrophotometry according to the method described by Chapman and Pratt (1978).
Stress relief curves can be made using leaf disks floated in .2mM EDTA. Ion release can follow a characteristic kinetic if salinity did not reach lethal doses. The release is apportioned to disk content that is made at the end of the experiment. Flame photometry for sodium would suffice if you assume 1:1 chloride contribution or you can use wet microchemistry for chlorine as well pX or ion chromatography. KCl and Na2SO4 treatments can reveal an anionic damage that although described, is quite rare.
A more simple method consists in putting your leaf in an eppendorf, homogenize it with a plastic rod and centrifuge it. If having a large number of samples, you can freeze them, and processes them as indicated before. Take an aliquot of the supernatant and make the appropiate dilutions for measuring Na (and K) by flame photometry and Cl by using a chlorine meter or a commercial assay kit for Cl.
Digest the dried ground material (0.5 g) of shoots or roots in concentrated HNO3 (5 ml) at 100 and than at 150ο C in digestion tubes and then make volume of the extracted up to 50 ml in the volumetric flask. Filter the extract and use it for the determination of mineral nutrients concentrations. Determine the dissolved amount of sodium, potassium and calcium using flame photometer and magnesium, manganese, iron and cadmium with atomic absorption spectrophotometer.
The suggestion I made comes from the need to understand if the salinity level was reversible or not. If a leaf disk is able to exchange sodium is in a condition that is not lethal. All given methods are good in principle but often soil drainage is attenuating salinity and a test for recovery culd be necessary to monitor influx-efflux ratios.
The same method I recommend 4 years ago is valid. Sometimes you need to estimate if salinity produces a reduction or an increase in leaf water content. In that case, you should weigh your leaf, dry it (oven 60-70ºC. 48h), weigh it again to estimate water content) and extract K & Na with hot distilled water (1 h, 90ºC). Then, filter the extract, dilute with distilled water to a known volume and measure cations by flame phtometry (or any other method yo have available).