Step 1: Install the game in Wine.
If you try to play the game in Wine, well... DOSBox doesn't play very nice with Wine. That's not a problem, because there's a native Linux version of DOSBox.

Step 2: Copy the game from Wine's directory (usually ~/.wine/drive_c/GOG Games/) to a more convenient place, like ~/dosgames/.

Step 3: Install DOSBox.

Step 4: Run DOSBox. In DOSBox, type:
Mount your C drive ("mount c [wherever you put the game]")
cd into the game directory
Run the setup program of the games, or the retro DOS music won't work properly (or at all).

Step 5: Quit the setup program and start the game.

The Windows (1998) versions have to be run in Wine itself, and they've got a few issues to work out.