It can be directly synthesized by the neutralization of sodium carbonate or sodium hydroxide with citric acid, but several disadvantages may occur, such as the speed of reaction and quality of the final product.

The following manufacturing process was came up by a China manufacturer with better output (1):

Obtain calcium citrate by reacting calcium carbonate and/or calcium hydroxide with citric acid.
Calcium citrate reacts with citric acid further to produce calcium hydrogen citrate and/or calcium dihydrogen citrate.
Then neutralize with the sodium carbonate and/or the sodium hydroxide to produce sodium citrate.
Specification
Other names   
Sodium citrate tribasic dihydrate or dehydrate
CAS number   
68-04-2 (anhydrous)
6132-04-3 (dihydrate)
Chemical formula   
C6H5O7Na3 (anhydrous)
C6H5O7Na3·2H2O (dihydrate)
Molecular weight   
258.07 (anhydrous)
294.10 (dihydrate)
Properties
Appearance
Crystalline white powder or crystals.

Solubility
Soluble in water (1g/1.5ml, 25°C), insoluble in ethanol.

PKa
Sodium citrate is the base of citric acid, which is a weak organic acid with three carboxylic acid groups and as a result it dissociates three H+, and with three PKa values, PKa1 = 3.14, PKa2 = 4.77 and PKa3 = 6.39.

PH
7.5 to 9.0 (5 % aqueous solution) (2)