For timetables of all trains and inter-city buses within Czechia as well as between Czechia and its neighboring countries, use this excellent website: idos.cz. Available in Czech, English and German (you can change the language in the lower side of the page) the website gives you precise information about the connections. If you have a student ID, show it when buying tickets and you will often receive a discount.
The nearest international airports are in Brno (Letiště Brno-Tuřany, BRQ) and Ostrava (Letiště Leoše Janáčka Ostrava, OSR) but there are not many flights to these destinations. A more practical option is to fly to Prague (Letiště Václava Havla Praha, PRG), but also Bratislava (Letisko M. R. Štefánika, BTS) and Vienna (Flughafen Wien-Schwechat, VIE) are well served by budget airlines (Ryanair, Wizz Air, Transavia, Volotea) and with easy reach of Kroměříž, via Brno.
From specific towns
At idos.cz search for connections from "Praha" to "Kroměříž".
The Czech language
Top Tip: learn a few basic phrases in Czech before you arrive. E@I co-created a website for learning Czech, and you might find these phrases useful: https://mluvtecesky.net/useful_phrases.