As a christian trying to expand into land ruled by other christians, a quick way is with claimants, such as the ruler's brother who didn't inherit. If you find a claimant and get them in your court, you can grant them land to make them your vassal. Then you can declare war for their claim and if the title you are claiming is a lower tier than yours (such as a claim on a county when you are a duke) then the claimant will remain your vassal after you win the war for their claim.

You can find current claimants to a title by going to its title page, there will be a claimants tab.

You can also try to marry into claims by marrying your ruler or heir to children of the ruler of the title you want, or try to set up a direct inheritance, though that's a longer term strategy.