Unlike the DOS window in Windows 2000, XP and Vista, DOSBox exactly emulates a full screen DOS session. Hence it doesn't support scrolling up and down. However, MS-DOS included a program to allow you to 'press any key' to scroll down called MORE.COM. This is how to do it on Windows:
Try and find a copy of MORE.COM from MS-DOS 5.0 (good luck) or MORE.EXE from FreeDOS (easy)
Put it in C:\C
Edit C:\Program Files\Dosbox\dosbox.conf in Notepad
Go to the bottom of the file, where it reads [autoexec]. Add to it or change it to read:
[autoexec]
MOUNT C C:\C
PATH=%PATH%;C:\

Save it, close DOSBox and then re-open DOSbox.
Now, say you wanted to use this command:
C:\> type readme.txt

Instead type this:
C:\> type readme.txt | more