A unix system's text-mode console can usually be accessed through a TTY device. On Linux, you'd normally access /dev/console or /dev/ttyN, where "N" is a number starting with 1. This page gives a pretty comprehensive description of the TTY devices representing the Linux console.
TTY devices have owners and file permissions like any other file, and these things can restrict who can access the TTY device. For example, on my system I see:
$ ls -l /dev/console
crw------- 1 myid staff 0, 0 Oct 27 2014 /dev/console
Right now, I own the console device, and permissions are set to 600, which means that only my account and root can write to it. It's normal for ownership of the console to belong to the account logged into the console at the moment.
Assuming you can access the relevant TTY device--because you're root, or you own the device, or the permissions are set to let you access it--then you can read or write to it like any other character device:
$ tail -f /var/log/messages > /dev/console
This command for example would run
tail, writing the output to the console device.