Storing Luggage Before/After Overnight Train?

Most major train stations have luggage storage, often coin-operated lockers. Park your bags there until it's time for the train, or at your arrival station until you go to your hotel/apartment. Hotels often will hold your bags until check in.

Checking in and out of the hotel room is separate from bag storage in their closet, normally free and available all day. You just have to choose whether the hotel or the train station is a more convenient location for you to return to. If your Prague hotel is located near sightseeing, it probably will be more convenient than the train station. Your hotel can call you a taxi to the train station; expect to pay about 300 Kc. (Prague station has lockers, so there should not be a line to retrieve luggage, which you can find in stations with a staffed storage office.)

As long as you're staying in a hotel and not an apartment, it's usually not a problem to store your bags after check-out or before check-in. And the only place that I've seen charge for this was the Easyhotel in Budapest, where it's part of their business model; other places have always done it for free.

As Laura says, you should determine if it's more convenient to use your Prague hotel or the Prague train station for bag storage before departure.

You only need to be on the train before it leaves, so if you want to cut it close, you can get there with just enough time to find your track, show your ticket, and hop on. Realistically, you'll want to get there at least 15 minutes beforehand; if you need to retrieve bags from a locker, use the restroom, buy food for the journey, etc, or if you move more slowly for any reason, allow more time.

Most stations have lockers(but they are small), Yet all hotels will store your luggage even after checkout so just leave them in the hotel... then pick them up before travelling.

The train station in Prague has big lockers even the small ones can take 2 decent sized bags. They cosy 80kc last time I used them, there is a machine to get change from in the locker area but the larges note it takes is 200kc.
The locker area is on the lower lever of the station on the far left hand side as you face the platforms.
As you are leaving from the Train station makes sense to leave your bags there for the day once checked out of your hotel. Easy to get to various sites from the Station.