Employee's background Verification includes everything about background like employment details, educational Qualification details, family details etc etc.
For employment verification,You may write to the HR of the previous company with details like designation, DOJ, employment duration,salary, LDW etc etc which have been provided by the new joinee. You may attach the scan copy of salary slip , relieving/resignation letter etc for verification of the documents.
Remember, always collect HR mail ID/contact number through your own source. You may call the HR department by finding number through Internet and may ask their mail ID for verification. Don't ask the new joinee to provide the same as he may give details of his known one.
In case of educational Qualification verification, you may approach respective institutions. And for family details verification, you may collect required documents and get it verified from respective authorities.
Hope this will be helpful for you.