A good way to approach this question is to ask: How many boys are going?
If the answer is only one, then the subject is singular.
Let's take a look at each sentence:One of the boys has agreed to go.
Which boy? Well, whichever boy it is, there is only one boy. Therefore, the subject is singular.Stan is among one of the boys who have agreed to go.
Now, Stan is one of a few boys. Therefore the subject is plural. Many of the boys have...
How many are there? More than one. Therefore the subject is plural.Few of the boys have agreed...
'Few' also implies more than one (i.e. John, Stan, Mike) so we must use the plural.
Let me know if that helps. If not, I can provide some more examples
Magoosh Test Prep