There is only one regular train from Kiev to Kherson.

101/102 - it starts from Kiev at 21:44 and arrives to Kherson railway station at 10:15.

If you will need to go from Kherson to Kiev - it starts from Kherson at 20:36 and arrives to Kiev at 07:39.

This service shows other trains from Kiev to Kherson, but they are only summer trains.

Here aproximate prices for tickets from Kiev to Kherson:
1st class sleeping car (has sleeping places for 2 persons, in russian pronouncing like “spal’nyi wagon”) - 330 ua grivnas;
2nd class (has sleeping places for 4 persons) [in russian pronouncing like “coupe”] - about 100 grivnas
3rd class (has sleeping places for 6 persons) [in russian pronouncing like “platzkart” or “platzkartnyi wagon”] - about 70 grivnas.

P.S. But if you dont have any time for waiting a train or would like to go from Kiev to Kherson as soon as possible, we can transfer you from Kiev to Kherson by comfortable car with a professional driver.