Q:

Salesforce Validation Rule

I have a requirement that in Filed client_Logo__c(URL) whenever user enters any URL : IF it dosen't begin with http or https then it must throw a validation error.

A:

Welcome to the exchange!
Have a look at the following link for some more in-depth explanation Click me!
For your case, if this is a default field, create a Validation Rule on your object. 
Error Condition Formula

NOT(
   OR(
      BEGINS( client_Logo__c, "http"), 
      BEGINS( client_Logo__c, "https"),
      ISBLANK( client_Logo__c )
   )
)

The rest (Rule Name, Error message) can be whatever you like
Edited:
Updated formula for further requirements
Have a look at the following
Examples of Validation Rules

Create Validation Rules
 - Trailhead

