[SalesForce] Call pagereference method from Trigger

All you need to do is change your current code to use the List<Category__c>> (i.e. Trigger.new) that you've passed into your method rather than referencing Trigger.new directly (which you can do, but then your class won't work outside of a trigger context).

I've also renamed a couple of your variables and formatted your code to make it easier to see what is going on:

public with sharing class CategoryHelper 
{   
    public static void ValidateCategories(LIST<Category__c> newRecords)
    {                                                                                             
        List<Category__c> existingRecords = [select id, Type__c from Category__c where Type__c != null]; 

        for(Category__c c : newRecords)
        {
            if(c.Type__c != null)
            {
                for(Category__c existrecord : existingRecords)
                {
                    if(existrecord.Type_of_Risk__c == c.Type_of_Risk__c 
                        || existrecord.Type__c == 'Cost' 
                        && c.Type__c == '%Cost'
                        || existrecord.Type__c == 'Time' 
                        && c.Type__c == '%Time'
                        || existrecord.Type__c == '%Cost' 
                        && c.Type__c == 'Cost'|| 
                        existrecord.Type__c == '%Time' 
                        && c.Type__c == 'Time')
                    {
                        c.Type__c.adderror('Type is already used please select another one.');
                    }
                }
            }
        }
    }
}

I'm not sure where you're going with this because the code you posted is pretty vague. Maybe you could make this a static method if you are only calling the PageReference exactly after you're instantiating the object. Here's a way to expedite the call of an instance method. This one goes to a new opportunity.

public class A
{
  public PageReference save()
  {
    return (new B()).pay();
  }
}

public class B
{
  public PageReference pay()
  {
    PageReference pageRef = new PageReference('/006/e');
    pageRef.setRedirect(true);
    return pageRef;
  }
}