public without sharing class SDPController {
    public List<Account> PAISchools = new List<Account>();
	
    public SDPController(){ 
		//1 - get ID from url, I suppose this controller is used for some VF page and you need insert id into url as parameter (like: /apex/vfpagename?id=someId)
		idString = ApexPages.currentPage().getParameters().get('id')
    }

    public List<SelectOption> PAIList{
        get{
			//2 - then you need to use Id from url to query proper account
            PAISchools = [Select Account.Name, Account.Id From Account Where Account.ParentId =: idFromUrl];
            
            PAIList = new List<SelectOption>();
            
            for(Account temp : PAISchools){
                PAIList.add(new SelectOption(temp.id, temp.Name));
            }
            return PAIList;
        }
        set;    
    }
    
    public String idString{get;set;}
    
	public PageReference saveform(){
  		update PAISchools ; // helps in saving the record
		PageReference pageRef = new PageReference('https://dev2-dor.cs22.force.com/eportfolio/LPRegistration?code='+idString);
		pageRef.setRedirect(true);
		return pageRef;
	}
    
    public PageReference signin(){
        PageReference signIn = new PageReference('https://dev2-dor.cs22.force.com/eportfolio/motivislp__LPSignIn');
        signIn.setRedirect(true);
        return signIn;
    }

}

@isTest
public class TestSDPController {
    
    public static testMethod void testSDP() {  
       
	   //3 do not hardcode ID, never! create test data every time
	   Account parentAcc = new Account(name= 'Testing parent');
       insert parentAcc;
	   
       Account childAcc = new Account(name= 'Testing child', ParentId= parentAcc.Id);
       insert childAcc;
       
       Test.startTest();
       PageReference testPage = Page.SchoolSelect2;
        Test.setCurrentPage(testPage);
		
		//4 - not why is this here, becouse there is no `Url` in controller
        testPage.getUrl();
		
		//5 - you use id of created child account, to test your VF page
		ApexPages.currentPage().getParameters().put('id', childAcc.Id);
        
        SDPController sdp = new SDPController();
			//6 - do not forget to assert results you get, to make sure your test is ok !! ;)
			List<SelectOption> selectOpt = sdp.PAIList();
        	sdp.saveform();
			spd.signin();
        Test.stopTest();   
     }
}