Make sure that you assume the worst about every player in a game (not about the person you're playing, but about their intentions within the game). This isn't a morality tale. Civilization is about the pursuit of victory, and you aren't being judged as a good guy or a bad guy. Someone who stays on your side for 150 turns isn't any more likely to help you than your worst enemy once the end of the game approaches.
Your point score isn't a way to intimidate anyone; it's an invitation. Having tons of wonders and large cities only means that you're worth conquering. Never leave any border in your nation exposed because you think that the player over there isn't going to fight you. It's true that they might not, but don't assume it. Keep at least enough defensive forces nearby to deter or at least slow down an attacker before they can get anything valuable.
Fortified units in rough terrain and ranged units in cities are both wonderful for this task. Try not to use too many troops, as that is a costly endeavor. Have enough people on hand to rival the number of enemies you're seeing anywhere near the border in question. Is it vacant? Well, then you should be the one attacking. See several troops in the vicinity? Keep a few people ready. See huge piles of units over there? Get ready for a fight, and take a long look at your other borders, too. People won't always attack by themselves (this is also true of the computer).
Rule the Waves, Watch the Shores
Naval forces can bring a city's defenses down very quickly. Fast naval movement allows units to approach a city and bombard it on the city turn, even fairly early in the game. The mix of a single fast unit and a good naval attack can topple a coastal city on Turn 1 of a war.
Keep your navy prepared for war if you have any exposed coastal cities. Leave them at the edge of your borders so that nothing gets close enough to assault your cities without your knowledge. Don't let anyone push too close, even during times of peace.
Fight in Bursts
A common weakness of conquerors, especially in single-player games, is to reach a certain point with their nation and start eternal warfare against the rest of the world. This is not a good idea, especially in multiplayer games. You're unlikely to get so much of a lead against most foes that it's safe to rampage against everyone. People have more time to react, prepare defenses, forge alliances against you, and repel your attack.
Not every war has to beat an epic conquest. If you see an opportunity to get something good, seize that. Humans aren't like the AI. Other players won't always turn on you when you make a nasty war against another nation. "I would have done the same thing" comes into play a fair bit.
Usually, human diplomatic issues are entirely determined by positioning, power, and mind games. Act friendly while doing foul deeds, and you might get away with murder.
Be on the lookout for key opportunities to start a skirmish. See colonists without good enough escorts? Workers and improvements that aren't guarded? Weak cities? Open borders? These are all good reasons to start a war. Even if you only get one city, that is a huge edge on your opponent.
Every Turn Counts
When building your army, assume that your target knows what's coming and is preparing a proper defense. Never approach an enemy city with the mindset that defenders won't arrive. Be ready for air units to rebase, defensive buildings to be purchased, and new units to race along the roads. The city you see ahead rarely appears as weak on Turn 3 of a war as they do on Turn 1. Every single moment matters.
Count on enemies to make smart decisions, and simply be happy when they don't.
You Two Go ahead and Fight
The oldest trick in the book is to have your enemies fight each other. Humans are extremely susceptible to mind games. Point out when another player has the most points. Warn others, with "genuine" concern, if anyone has too many virtues or too large a military. Joining forces against larger targets is wise, but it's better for your civilization if you deceive others into fighting without demanding your involvement in the process.
Don't let other people do this to you. Never start a war out of fear. Do it because you have a better chance of winning the game by proceeding. When other people communicate with you during a game, be polite. Be funny. Have a good time with them. And, ignore almost everything that they say, unless it has direct use for you and has provable benefits.
There are some opponents that you can't beat militarily. They might have better land, a larger military, Might virtues, or more experience as a tactical leader. Whatever the case, realize that you cannot win a traditional battle, and stop trying to do this. Instead, move the goalposts, and try a different type of battle.
In asymmetric warfare, you don't try to win by defeating your enemy. Instead, you win by doing more damage to them than they're willing to take. End wars by crippling your adversaries' economies. Destroy their tile improvements, kill their trade units, steal workers, or lure them back into your defensive chokepoints and kill their units. This way, you can hurt them even if you cannot take a single one of their cities.
This bitter pill is a way to encourage neighbors to fight other targets. Your first goal in a war is to win. The second goal is to not lose. Fast raiders, groups of cheaper melee units near cities, and stacked defensive bonuses are all ways to improve this process.