AnyTrain lets you buy train tickets online. You can book a Kharkiv - Kyiv ticket at a good price from anywhere with an internet connection. An e-ticket can often replace the traditional paper ticket from the ticket office, and buying online saves time and spares you the queues at the station.
Note that not every train accepts electronic boarding. There are three types of ticket: with a QR code (no need to print it), with a booking code (exchanged for a ticket at the station if required) and tickets that must be exchanged at the station ticket office.
To buy a Kharkiv - Kyiv ticket on AnyTrain, start by choosing your travel date. If you only want to check the timetable between Kharkiv and Kyiv, remember that it changes regularly, so check which trains are running before you buy.