Rules in the de jure realm, especially counts, may agree to become your vassal without a fight.
You get a de jure CB on the rest of the de jure counties.
The remnants of the old kingdom will probably be fractured into different realms.
This tends to make conquering the rest of the kingdom easier because
Once you gain more than 50% of the de jure counties in the target kingdom, you can usurp the kingdom title.
Especially if you cannot marry into a claim on the kingdom, consider pressing claims on duchy titles in the target kingdom.
The significance is that you can declare war on rebelling vassals without penalty even if you have a truce against the liege (king, in this example)
If vassals of the target king are rebelling, you can declare war on a rebel.
Waiting until your heir inherits both your kingdom and the claim on your target kingdom, and can press the claim playing as your heir.
Pressing the claim of your heir's parent, setting up your heir to inherit both kingdoms.
With claims, you may have a choice between For example, have your male heir (or you, if you are male and do not have a male heir) marry a princess with an inheritable claim.
As mentioned by svick, position a future heir of your kingdom to inherit a claim on the target kingdom.
Assuming a child is born and compatible succession laws, your heir will rule both kingdoms.
The most direct way: If the target kingdom is ruled by an unmarried queen, your male heir (or you, if you are male and do not have a male heir) can marry the queen.
Position a future heir of your kingdom to inherit the target kingdom.
On the other hand, you may be able to use assassination or a plot to arrange a timely death. Ways to use Love, not War to gain a kingdomīeware, an untimely death can spoil your plans.
If you are playing as a pagan (requires The Old Gods expansion), the become king of ambition gives you a CB against realms inside the de jure territory of the kingdom.
If you have a claim on the kingdom, you can press your claim.
If the target king is a heretic of your religion, your religious head might declare a crusade against the king.
If you are invading realm that is larger (more holdings) than yours, you can use the Invasion CB.
As mentioned by svick, if you are an emperor, you can press a claim on the kingdom title for a relative or vassal, and upon winning, the claimant will be your vassal.
Ways to literally invade the entire kingdom at once (You can break a truce, but the penalty is harsh) There are a couple of things that make conquering a kingdom hard.