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U ChauhanU Chauhan 

Test Class for visualforce page

// Please help me in writing test class for this custome controller in
// visualforce page
public class Cont_ServiceFieldManagement {
    list<String> sendingTo =new list<string>();
    list<id> idListAgent=new list<id>();
    set<id> idsetCustomer=new set<id>();
    public string agentId{get;set;}
    public list<field_Agent__c> agent{get;set;}
    public string agentCity {get;set;}
    public list<Customer_Service__c> orders{get;set;}
    public Customer_Service__c customer{get;set;}
    public string ProductName{get;set;}
    public date PurchaseDate{get;set;}
    public string serviceNeeded{get;set;}
    public string customerName{get;set;}
    public string phone{get;set;}
    public string email{get;set;}
    public string city{get;set;}
    public string address{get;set;}
    
    public Cont_ServiceFieldManagement(){
        
    }
    public pagereference save(){
        Customer_Service__c cust=new Customer_Service__c();
        cust.Product_Name__c=ProductName;
        cust.Purchase_Date__c=PurchaseDate;
        cust.Service_Required__c=serviceNeeded;
        cust.Customer_Name__c=customerName;
        cust.Phone__c=phone;
        cust.Email__c=email;
        cust.Submission_Date__c=date.today();
        cust.City__c=city;
        cust.Address__c=address;
        insert cust;
        PageReference tempPage = ApexPages.currentPage();            
        tempPage.setRedirect(true);
        return tempPage;
    }
    public pagereference cancel(){
        PageReference tempPage = ApexPages.currentPage();            
        tempPage.setRedirect(true);
        return tempPage;
        
    }
    public pagereference getorders(){
        orders=[select id,Product_Name__c,Customer_Name__c,city__c,field_agent__c from Customer_Service__c where city__c=:agentCity and field_agent__c=null];
        for(Customer_Service__c cust:orders){
                idsetCustomer.add(cust.id);
            
        }
        return null;
    }
    public pagereference getAgent(){
       agent=[select id,name,phone__c,email__c,city__c from field_agent__c where city__c=:agentCity] ;
        for(field_agent__c ag:agent){
                idListAgent.add(ag.id);
            sendingTo.add(ag.email__c);
        }
        return null;
    }
    public pagereference AssignAgent(){
        list<Customer_Service__c> custList=new list<Customer_Service__c>();
        list<Customer_Service__c> customerList=[select id,Product_Name__c,field_agent__c,status__c from Customer_Service__c where id in:idsetCustomer];
        for(Customer_Service__c cust:customerList){
            cust.Field_Agent__c=idListAgent[0];
            cust.status__c='Assigned';
             custList.add(cust);  
        }
        
        update custList;
        return null;
    }
    public pagereference sendEmail(){
        Messaging.SingleEmailMessage semail = new Messaging.SingleEmailMessage();
        semail.setToAddresses(sendingTo);
        semail.setSubject('New Work Order Assigned To You!!!');
        semail.setPlainTextBody('Hello!!!!! You have been assigned to new work orders');
        Messaging.sendEmail(new Messaging.SingleEmailMessage[] {semail});
        PageReference tempPage = ApexPages.currentPage();            
        tempPage.setRedirect(true);
        return tempPage;
   }
}
SwethaSwetha (Salesforce Developers) 
HI Chauhan,
Since this code is huge and requires an understanding of your implementation, it might not be possible to provide exact edit suggestions. However, the example listed in  https://jayakrishnasfdc.wordpress.com/2021/01/02/apex-test-class-for-visual-force-vf-pages-controller-extension/ should help you get started.
https://salesforce.stackexchange.com/questions/244788/how-do-i-write-an-apex-unit-test
https://developer.salesforce.com/forums/?id=9060G000000Bj8MQAS

If this information helps, please mark the answer as best.Thank you