Train from Munich to Prague - Timing before Train Departs

Czech Republic and Germany are both part of the Schengen Area - open borders. There probably won't be any security to get on the train, though there may be a passport check on the train (haven't crossed this border, so I don't know). The UK is not part of Schengen, so when you take a train to Paris from London, you have to go through immigration, plus there has always been more worry about security there - more complicated.

If you don't have reserved seats on the train, I'd get there a tad earlier to make sure you get decent seats. Otherwise, I'd arrive at the station no more than 15 minutes before departure, maybe 30 minutes to make it completely low stress, but I certainly wouldn't get there an hour early, especially that early in the morning.

Many, perhaps most, train stations do not post the departure platforms until about 20-30 minutes before departure. Seating in the lobby iss often in short supply. However, if you can step lively once the info goes up, you will have a better chance at securing space for luggage.
Schengen countries are border-free but, in these days of heightened security, a spot check of some sort might be a possibility to keep in mind for your schedule.

I was wondering how early do we need to get to the train station before our train leaves since this is an international train going from Munich, Germany to Prague, Czech Republic?

Technically, that's rather a combination of two local trains, one run by the ALEX (Länderbahn) company, the other by CD. No check-in procedure, no security, passport inspection and the like. The train sits in the station usually 20min before departure (on the northernmost platform in the main hall) - just board and secure your seat. And please read the signs on the cars carefully, since ALX 353 carries cars going to Hof (numbered ALX 84103), which will be detached in Schwandorf. The cars to Prag are usually in the front part of the train. have you booked facing seats? That would be good, because the train changes direction in Regensburg and Schwandorf.

Most trains in Europe, even international ones, have no check-in or security check at all. The only exceptions are Eurostar between London, Lille, Paris, and Brussels, which has airline-style check-in, border controls, and security; Spanish AVE high-speed trains, which have a security check; and Thalys trains between Paris, Brussels, Amsterdam, and Cologne, which sometimes have security checks after a failed terrorist attack a few years ago.

Not in Germany since you do know the track from which the train departs but still the electronic board if there is a change. Most likely it will be the track (Gleis 23 ?) closest to the Yorma food market.

For technical reasons, the ALEX trains always leave from track 24 to 26. Track 26 is that one opposite the Yorma food stall. You can determine the actual track way in advance: there are printed (yellow) tables that show the track of a train, then there is a big electronic display in the central hall and finally there is a electronic display at the beginning of each track, which shows the actual train and the next one leaving from that track. It's not like Italy, where a train is announced often just a few minutes in advance.

You guys are AMAZING!! Thank you so much for all of the help!! :)

Good... it is track 26. I only know how to get there, ie next to Yorma. Thanks.