Since the Pompey patch (1.1), the console is disabled by default. To enable it, you need to launch the game in the debug mode, Which you can do in multiple ways depending on your launcher such as:
On Steam: right-click the game, choose Properties, Set Launch Options, add "-debug_mode"
On Windows: create a shortcut for the game, right-click it, choose Properties and in the Target field add "-debug_mode" (remove the quotation marks) at the end
On GOG: right-click the game, choose Settings, check "Add command line arguments" and enter "debug_mode"
On GOG Galaxy 2.0: In the game page, select the Settings button next to the Play button at the top of the page, open the Manage installation submenu and select Configure…. In the new window, make sure the Launch parameters Custom executables / arguments is ticked at the bottom of the page. You can duplicate the "startgame" executable and type -debug_mode into the Arguments field.