What is the minimum required for a Resolution to be passed?

Solution 1:

There must be as least one more yay vote than there are nay votes for a resolution to pass. Abstaining from voting on a particular resolution has no effect on the outcome as you are not voting either way.

In order to know how many delegates to commit you must make an educated guess about the votes of your rivals. You can place a Spy as a Diplomat in a rival's capital to see their upcoming votes.

Solution 2:

For normal World Congress resolutions, the vote is a simple majority vote. If there is 1 more "yea" than "nay", then the vote passes.

The "World Leader" resolution is the only exception (Diplomatic Victory). This requires a minimum number of votes that is set based on the number of Civilizations and City States in the game (according to the in-game Civilopedia, and my experience). However the World Leader vote will not happen until the United Nations is built (and periodically afterwards), and cannot be manually initiated.