Train from Budapest to Brno

While you don't need to, it is better to do so: you can get $20 advance tickets online through the Czech Railways (CD.CZ).
Beware that the Brno main train station is closed, so trains arrive at Brno Dolní Nadrazi Station, a bit further from the center. Also, in Budapest, the train does not leave from the main Keleti station, but from the smaller Nyugati station.

1. If you are departing from Hungary, I would purchase my tickets from the Hungarian train company. MAV.
2. The tickets purchased on line will be somewhat cheaper. MAV offers that. I am fairly certain that you can purchase the day before and get the same discount. But, since you are asking such a basic question you might feel more comfortable at a ticket office. You can go to either Keleti or Nyugati stations for that.
3. Nyugati is not smaller than Keleti. Okay, it is. Nyugati has 17 platforms while Keleti has 18. Both are worth the visit for the architecture.
   

Here is how to use the Hungarian Rail (MAV) site to purchase tickets

https://www.seat61.com/websites/mav-start.htm

And this is interesting reading

https://welovebudapest.com/en/2017/01/02/the-shining-history-of-budapests-nyugati-railway-station/

As is

https://welovebudapest.com/en/2014/08/28/explore-the-subterranean-society-of-pests-nyugati-underpass/

But dont be afraid, very safe, but a tour not many tourists get.

Hello from Wisconsin,
cd.cz

that is the website to visit. Excellent place to buy tickets.

wayneiNWI