Unlike Starcraft, there is no real Observer mode in Rome: Total War. So, it's slightly less-convenient for an extra person to watch a game LIVE when he/she is not a participant. That said, you can still observe a game if you follow a few steps. Here are a few directives to know if you wish to observe a game:
01. PERMISSION FOR AN EXTRA SLOT
Ask if it's okay for you to observe a game. It's easier to observe a game between 2 online players if you know them. If you get permission, then the Host can re-make the game with an extra slot (reserved for you). Also keep in mind that, during a tournament, a person might not want you watching if it could jeopardize their "military secrets" to you, a potential opponent in the tournament.
02. IF YOUR CONNECTION IS SLOW, DO NOT OBSERVE
If your computer connection is slow (and you know this), do not observe a game because you'll only slow their game down.
03. DON'T AFFECT THE MAP BALANCE
If the map is completely equal when divided (i.e. the Syrian Flats, Grassy Flatlands, etc), then it shouldn't be an issue if you tag-along. But if the map is uneven (i.e. the Macedonian Ruins), then your very presence could seriously destroy the balance of the participants' starting positions.
04. PICK A FACTION THAT NO ONE WILL USE
The observer should pick a faction that nobody is going to use. You don't want to observe a game with Carthage if one of the players wants to use them.
05. THE OBSERVER(S) SHOULD NOT BE ON THE SAME TEAM AS ANY OF THE COMBATANTS
The observer should change his Team Number so that he's on a team by himself. If the observer is on the same team as one of the players, then that unfortunate player will have less money to spend.
06. THE OBSERVERS ARMY SHALL CONSIST OF 1 PEASANT
Whenever the observer picks his faction, his army should consist of only 1 Peasant.
07. POSITION YOUR ARMY NEXT TO THE EMERGENCY EXIT
During deployment, the observer should deploy his Peasant near the edge of the map (ready to exit). And then, once the battle starts, the observer should "surrender"" so that his 1 Peasant unit leaves the battlefield immediately (unable to get in the way of the other players' units).
08. FRIENDLY REMINDER TO THE PLAYERS (DURING DEPLOYMENT)
Be courteous and remind your opponents before a battle not to deploy facing your deployment line. It's kind of annoying when an actual participant deploys facing the direction of the observer. If such a mistake happens, then that player will have to waste time re-facing his army.
09. SILENCE IS GOLDEN
Do not chat during a battle to the players. If there is another observer with you, then you (the observers) should send messages directly to each other if you want to chat (and not to the players who are concentrating).
10. THE OBSERVER VERSUS THE TACTICAL ADVISOR
Remember, you're there as an observer: not as a tactical advisor(!). Don't give advice to the participant(s) before or during a game. It's so freaking annoying when the observer starts giving advice about how to fight a particular matchup or player or map or whatever. The only "advice" you should give is the friendly reminder not to deploy facing your battle-line.
11. WHEN TO SAY "GG"
Yes, even the observer should say "gg." But "gg" should only be said AFTER the game. Do NOT say "gg" if a player is simply winning at the moment or if you think a particular player is going to win. It's considered poor-manners to announce a victory unless a player has admitted defeat or until the announcer says the game is over (or if you see the results screen).