Can anyone help me how to write test class for the below code.

I did some  chages in your Main  Ctrl but logic are same. Replace your Ctrl with Following and copy & paste test class in your org.

//Main Class
public class CreatingandupdatingaccountcontactRecords {
    public string accountName {get;set;}
    public string contactName {get;set;}
    public string emailId     {get;set;} 
    public string phoneNumber {get;set;}   
    List<Account> accountList   = new List<Account>(); 
    List<Account> upsertAccount = new List<Account>();
    List<Contact> contactList   = new List<Contact>();
    List<Contact> upsertContact = new List<Contact>();
    public void checkAccountsandcontacts() {
        accountList = [select Name from Account where Name =:accountName];
        if(accountList.size() > 0) {
            for(Account  a : accountList ) {
                if(a.Name == accountName) {
                    a.Emai_id__c =emailId;
                    a.Phone = phoneNumber; 
                    upsertAccount.add(a);
                }
            }  
        }  
        else{ 
            Account newAccount = new Account();
            newAccount.Name = accountName;
            newAccount.Emai_id__c = emailId;
            newAccount.Phone = phoneNumber;
            upsertAccount.add(newAccount);
        } 
        upsert upsertAccount;
        contactList =[select LastName from contact where LastName =:contactName];
        if(contactList.size() > 0) {
            for(contact con : contactList) {
                if(con.LastName == contactName ) { 
                    con.Email = EmailId;  
                    con.Phone = phoneNumber;
                    for(Account a1 : accountList) {
                    con.AccountId = a1.Id;
                    }
                    upsertContact.add(con); 
                } 
            }
        }
        else{
            contact newcontact = new contact();
            newcontact.lastName = contactName;
            newcontact.phone = phonenumber;
            newcontact.Email = EmailId;
            for(Account acc:upsertAccount) {
                newcontact.AccountId = acc.Id;
            }
            upsertContact.add(newcontact);   
        }
        upsert upsertContact;  
        if(accountList.size() > 0){
        ApexPages.addmessage(new ApexPages.message(ApexPages.severity.info, 'Your record is updated successfully')); 
        }
        if(accountList.size() == 0){
          ApexPages.addmessage(new ApexPages.message(ApexPages.severity.info, 'Your record is created successfully'));  
        }
    }  
}

//Test Class
@istest
public class CreatingandupdatingaccountcontactRecordsTest {
    @istest
    public static void UnitTest() {
        Account Acc =New Account();
        Acc.Name = 'test';
        Acc.Phone = '9898989809';
         insert Acc;
         Contact Con =New Contact();
       Con.LastName = 'testCon';
        Con.Phone = Acc.Phone;
         insert Con;
       CreatingandupdatingaccountcontactRecords oCreatingandupdatingaccountcontactRecords = new CreatingandupdatingaccountcontactRecords();
        oCreatingandupdatingaccountcontactRecords.accountName = Acc.Name;
        oCreatingandupdatingaccountcontactRecords.contactName = Con.LastName;
        oCreatingandupdatingaccountcontactRecords.emailId = 'Test@test.com';
        oCreatingandupdatingaccountcontactRecords.phoneNumber =Acc.Phone;
        oCreatingandupdatingaccountcontactRecords.checkAccountsandcontacts();
    }
      @istest
    public static void UnitTest2() {
       CreatingandupdatingaccountcontactRecords oCreatingandupdatingaccountcontactRecords = new CreatingandupdatingaccountcontactRecords();
        oCreatingandupdatingaccountcontactRecords.accountName = 'test';
        oCreatingandupdatingaccountcontactRecords.contactName ='tescon';
        oCreatingandupdatingaccountcontactRecords.emailId = 'Test@test.com';
        oCreatingandupdatingaccountcontactRecords.phoneNumber ='09098798678';
        oCreatingandupdatingaccountcontactRecords.checkAccountsandcontacts();
    }
}

let me know if it helps you and marking it as best.