Add the highlighted test method in your class:

public class Activity {
    public Activity(ApexPages.StandardController controller){
    }
    List<Task> tsk = new List<Task>();
    public List<Task> getactivit()
    {
     tsk = [select Subject, Assign_To__c,Status, ActivityDate, Description, Action_Item__c from Task
     where WhatId =:ApexPages.CurrentPage().getParameters().get('id')];
     return tsk;
     }
     public static testmethod void testActivityClass(){
               
         Task t = new Task();
         t.OwnerId = UserInfo.getUserId();
         t.Subject='Send Out Notice To Vacate';
         t.Status='Not Started';
         t.Priority='Normal';
         t.Assign_To__c=NULL;
         t.Action_Item__c=NULL;
         insert t;
        
         ApexPages.StandardController con = new ApexPages.StandardController(t);
         Activity a = new Activity(con);
         List<Task> tsk = a.getactivit();
    }
 }

* You can also add this method in a separate class as follows

@isTest
 private class testActivityclass{
     static testmethod void testActivity(){
               
         Task t = new Task();
         t.OwnerId = UserInfo.getUserId();
         t.Subject='Send Out Notice To Vacate';
         t.Status='Not Started';
         t.Priority='Normal';
         t.Assign_To__c=NULL;
         t.Action_Item__c=NULL;
         insert t;
        
         ApexPages.StandardController con = new ApexPages.StandardController(t);
         Activity a = new Activity(con);
         List<Task> tsk = a.getactivit();
    }
}

You can refer to the following link for writing test class

http://wiki.developerforce.com/index.php/An_Introduction_to_Apex_Code_Test_Methods

Let me know if you face any difficulty..........

Hope this helps you.