Hi Amit,

Please try this trigger + apex class. Please note that in order to keep this simple for demostration purposes, this is not "Blukified" 

Create Apex Class - Your Name | Setup | Develop | Apex Classes: New

public class MyCustomObject_HDL_AIAU {
	public void OnInsert(List<MyCustomObject__c> newRecords,List<MyCustomObject__c> oldRec){
        updateRecord(newRecords,oldRec); 
    }
    public void OnUpdate(List<MyCustomObject__c> upRec,List<MyCustomObject__c> oldRec){
        updateRecord(upRec,oldRec); 
    }
    private void updateRecord(List<MyCustomObject__c> upRec,List<MyCustomObject__c> oldRec) {
    	/******************************************************************
        DECLARE
        ********************************************************************/
        Boolean IsNew = false;
        List<Contact> ContactsToAdd = new List<Contact>{};
        
        /******************************************************************
        * IDENTIFY IF OLD RECORDS HAS VALUE
        ********************************************************************/ 
        Boolean NewRecords=false;
        if(oldRec==null){
            NewRecords=true;
        }

       	for(MyCustomObject__c upRec1:upRec){	
			if(upRec1.Practice_ID__c!=null){
				
				/******************************************************************
			    * FUNCTION FOR ONLY NEW RECORDS  
				********************************************************************/ 
				Boolean NewRecordForRow=true;
	        	if(NewRecords==false){
		        	for(MyCustomObject__c oldRec1:oldRec){
		        		if(upRec1.Id == oldRec1.Id){
		        			NewRecordForRow=false;
		        		}	
			        }  
		        }
				/******************************
				* If Practice ID on the new record is populated:
				*******************************/
				if(NewRecordForRow==true){
					/******************************
					If the value in Practice ID is less than 5 digits, add zeroes to the left of the Practice ID when comparing.
					For example, if Practice ID is 123, try to find an account where Context ID contains ‘00123’. 
					Note: The value in Practice ID on the Custom object shouldn’t be modified.
					*******************************/
					String PracticeIdToCompare = upRec1.Practice_ID__c.trim();
					Integer PracticeIdToCompareLength = PracticeIdToCompare.length();
					if(PracticeIdToCompareLength<6){
						for (Integer i = 0; i < 6-PracticeIdToCompareLength; i++) {
			    				'0'+PracticeIdToCompare;
						}
					}

					/******************************
					* Try to find an existing account where Context ID(Text field) on the account contains the value of Practice ID(Text) on the Custom Object.
					*******************************/
					List<Account> SearchAccount = [SELECT Id,Context_ID__c FROM Account WHERE Context_ID__c =:PracticeIdToCompare  AND IsDeleted=false];
					if(!SearchAccount.IsEmpty()){
						
						for(Account SearchAccount1:SearchAccount){
							/******************************
							* After: If we are getting any matching Accounts then create some records like create contact related to Account etc.
							*******************************/
							Contact ContactToAdd = new Contact(
	               				 FirstName= 'John'
	                			,LastName='Doe'
	                			,AccountId=SearchAccount1.Id
	            			);
			            	ContactsToAdd.Add(ContactToAdd);
						}
					}
				}
		
			}
			
		}
		
		if(!ContactsToAdd.IsEmpty()){
			INSERT ContactsToAdd;
		}
    }
}

Then goto Your Name | Setup | Create | Objects | MyCustomObject | Trigers | New

trigger MyCustomObject_AIAU on MyCustomObject__c (after insert, after update) {
    MyCustomObject_HDL_AIAU handler = new MyCustomObject_HDL_AIAU ();    
  	if(Trigger.isInsert && Trigger.isAfter) {
   		handler.OnInsert(Trigger.new,Trigger.old);
   	}else if(Trigger.isUpdate && Trigger.isAfter) { 
    		handler.OnUpdate(Trigger.new,Trigger.old);
   	}	
}

 Let me know how you go :-)