For a player who wishes to exceed the cap with just built-in console commands, zz_addparty is definitely the way to go. But first I must share a warning:
If used to add a character that isn't currently a member of your party (either active or in camp), it may damage the continuity of your game. This is because this command basically accomplishes two things. First it adds companions that you've already hired to your active party, enabling you to exceed the cap. This is the effect we want. Nevertheless it also has a second effect. It may also be used to hire a companion that is not in your party and add them to your active party. This may be because you haven't yet encountered that character, or perhaps it may be because you've killed that character. This can be useful if you missed your opportunity to hire them or have since come to regret your firing or killing of them. If so, then by all means fee free to use this command for this second purpose as well. I simply recommend not using this command to add a character that you haven't yet encountered unless you're willing to miss their initial conversation/encounter.
There is a second serious issue that has less to do with this script than the single danger I've encountered when playing a game with "extra" characters. This is that the scripts used by the game to remove your companions at those places where you're meant to solo adventure (most notably the Fade) will fail to remove more than 3 characters. This can cause some significant problems. In my case the problem was that my companions failed to appear in their personal fade domains at the end of the fade quest. So I ended up going back and redoing large chunks of the Fade. This is why I always remove extra party members before entering a solo area these days. When I find the time I plan to track down the script function causing this issue and fix it.
Now with the warnings out of the way here is the syntax:
~runscript zz_addparty <companion>
where <companion> is the name of the companion you desire added to your active party.
This command will result in one of two specific behaviors depending on which character you hire with it. Some characters like Alistair, Dog & Morrigan will always appear next to the character without invoking the partypicker selection screen when they are chosen. Others such as Leliana and Sten will cause the game to enter the party picker where you can remove characters from your active party as well as add/edit them. Given that you can use the partypicker to remove characters, the safest way to remove extra characters once you exceed the cap is to invoke this command using one of the characters that will invoke the partypicker such as Sten or Leliana.