Weakening rival realms can make them easier to attack, or less likely to attack you.
Lowering vassal opinion
Vassals with low opinion will provide fewer troops, depending on crown authority minimums. They will also be more likely to join factions against their liege, which can result in civil war.
- Sow Dissent with your chancellor. Unfortunately, this fires infrequently, and may fire at a mayor (making him angry at the duke) rather than the duke (making him angry at the king).
- Assassinate popular rulers, especially if the heir has unpopular traits
or unpopular genes 
to add to their "short reign" penalty. - Assassinate happy vassals, especially
rulers. - Have vassals' heirs visit your court. When they inherit, they will have the full "short reign" penalty toward their "new" liege.
- Educate vassals' grandchildren as ambitious, envious, and of a different culture.
- Excommunicate the ruler if your religion has the mechanic.
Encouraging factions
Throwing your enemy's realm into civil war has many benefits:
- The faction is likely to fire when its army size is a close match, so the armies of the faction and the main realm are likely to obliterate each other.
- You can pick off pieces of each, with little concern for truces or them putting up a fight.
- A successful independence war will permanently weaken the realm, while giving you lots of easy pickings.
- (Without Conclave) A successful war to lower crown authority will reduce the realm's levies, as long as it does not have a popular ruler.
- And the next ruler may be tempted to raise crown authority when he cannot afford the "-30 increased crown authority" opinion penalty.
- A claimant faction war makes the title "contested", allowing you to press weak claims.
You can see who is currently in factions using your enemy's "realm tree" or "vassals" list. Hovering over each vassal will show what factions they are in. This can give you an idea of how close the realm is to civil war, although future faction membership is hard to predict.
Lower vassal opinion (see section above)
Assassinate vassals who cannot join factions:
- Prisoners
- Children, if they have adult heirs
- Vassals who have a "-5 discouraged from factionalism" opinion modifier of their liege, e.g. as a result of a visit from the liege's spymaster
- Vassals who have a non-aggression pact with their liege
Wipe the ruler's armies to increase faction power:
- Become hostile by raiding.
- Declare war to make them a tributary (only has a 1-year truce), but negotiate white peace or immediately release them if you intend to attack them again.
- Declare war on behalf of a claimant courtier, then have them killed to invalidate the war. The claimed title can be as small as a barony.
Taking sides in their civil wars
You can't actually join the war (on either side), but by declaring war on one of them, you get to be hostile to the armies of both.
You usually want the rebellion to succeed. A failed rebellion will give the ruler a "+25 crushed a major rebellion" opinion with his vassals, and allow him to consolidate power by revoking titles from the traitors. But if it is a claimant faction, see what you think of the claimant before deciding which side to fight on.
If you declare war on the rebelling faction, you do not have to bother winning your war, because it will end inconclusively when the rebellion ends. So, you usually want to declare war on the rebels, but attack the army of the non-rebels.
Other
Make pieces of their realm inherit into yours, if their laws do not prohibit it.
Encourage heresies within their religion by lowering its moral authority. After several decades, they will have to deal with dangerous revolts and may even lose territory to rebels. It is even possible that some vassals or the ruler will adopt the heresy, causing tension between them. This is a long-term gambit to use against an entire religion, rather than something to use against a single small realm.
If they have Gavelkind succession, break them up. This is best if they hold multiple primary titles (e.g. a double king), but useful even when it just splits up a king's demesne and sets up succession crises. Murder old wives so the men remarry and have more kids. Seduce their wives. If they have 4 daughters and 1 son (with agnatic-cognatic succession), murder the son.
If you can get a future heir into your court, educate them terribly. Aim for maximum incompatibility with their future vassals, especially in religion and culture, which affect membership in independence and claimant factions. (Depending on the situation, there may be more useful things you can do with the heir, such as marrying them into your family and co-inheriting their realm in the next generation.)
Destroy their demesne by choosing wargoals containing their personal counties.
Break their alliances. Hovering an alliance flag will tell you which married or betrothed couple is the basis for the alliance. Assassinating one of these characters will cause the alliance to break down. You can also invite a betrothed adult to your court and simply right-click them to break the betrothal. Alternatively, you can murder one of the rulers. The new ruler may be able to renegotiate the pact (based on the same existing marriage or betrothal), but is unlikely to do so.
Raid their lands. Never underestimate the power of raiding. All the money earned by you through raiding is money they'll be unable to use. Pillaging holdings can severely cripple both their tax income and levies.
If the enemy is Muslim, encourage decadence in their dynasty. Ensure they lose holy wars, instantly adding a large amount of decadence. Assassinate the top ruler until a child or decadent character is in place, so they can't ask relatives to straighten up. Murder old wives so the men remarry and have more kids.
Force tributaries. If your rival is undergoing a civil war or is otherwise weak from a recent war, bankruptcy or raiding, attempt to force tribute from them. This is especially worth it if they're a Merchant Republic or Feudal/Iqta (if you are tribal, a Feudal tributary gives a lot of money you otherwise get little of). Depending on their monthly income, it might be worth it to hire mercenaries, especially if you can force several tributaries at once.
Sabotage vassals. Most of the income and levies of a realm typically come from vassals. Sabotaging their vassals through assassinating economically or militarily strong vassals, raiding vassal demesne or destroying the trade posts of Merchant Republic vassals can greatly reduce tax or levy output given to the liege.
Pollute their bloodline. For example, allow your daughter to marry their heir. Keep in mind that this creates a NAP and may give their offspring claims on your titles.
Ask China to shatter them. For 5000 grace, you can ask China to invade a large realm and dismantle their higher titles. The realm must be within China's interaction range.