How can I get other civ to attack me?

The AI tends not to declare war, unless some combination of the following is true:

• You're close to winning (most of the spaceship built, etc)
• They have a significant military advantage (there's some locality to this, ie, if you shift your military away from the border with a powerful neighbor, they are more inclined to attack you, even though your overall military might is unchanged)
• You have poor relations with them (you denied requests for assistance, broke agreements, were aggressive towards city-states, etc)
• You have something that they want (ie, there's no more land and yours is convenient)

You don't need all of these for a declaration of war, however. You'll also note that being at war (whether you started it or not) is likely to increase the likelihood of more war against you. Your units are moving and concentrating away from your other neighbors, you're taking more land and are closer to victory, etc.

Therefore, there's not a lot of reliable ways to get your weaker neighbors to attack you, which won't also cause your stronger neighbors to also want to attack you.

My advice in this situation would be to find another civ who is not on good terms with one of the weaker civs, and make a deal with them to mutually declare war. Even better, find one that is not geographically close to the civ you wish to conquer, so that there's little to no risk that they'll take any cities you intend to capture. This ties up the "ally" civ, introduces some new political variables into the mix, and gives you a chance to conquer.

Another option is to build enough units that you can defend against the other civilizations' attacks, should they decide to come after you. Usually a couple of siege units and some infantry units per city is enough to repel an invasion from a neighboring civ. Then, just declare war, puff up your chest, and say something imposing and catchphrase-worthy. (ie, "Come at me, monsieur!" or "They can take our swordsmen... but they'll never... take... our CATAPULTS!")

Some tips for having another civilization declare war on you:

• Militaristic civilizations don't need much encouraging, especially if their military score is higher than yours (they lack tactics, so you can defeat them with a substantially reduced force). Unfortunately, a strong AI will wait until you declare war with a weaker neighbor, then backstab you.
• Land disputes are an easy way to escalate tensions with your neighbors, especially if your borders cut off a crucial path or you plant a city on their border, taking resources that they covet. If your borders touch theirs, a Great Artist or Great General can be used to steal land, which will definately escalate tensions towards war.
• With the Gods and Kings expansion, you can earn a lot of ire by sending religious units into their territory. Espionage can also be used to escalate tensions, and will inform you when a watched civilization is planning a sneak attack.
• Finally, if you have an ally civilization, you might be able to bribe a war between the two AI civilizations, then come to the assistance of your ally. In some cases, you can come to the defense of city-states that you have pledged to protect. If peace is negotiated and you haven't taken any of their cities, the AI might not even have any negative feelings towards you.