Enable custom tags for Contacts and Leads fields with master and lookup relatioships

I am trying create custom tags by creating a contact master-detail relationship and a lead lookup relationship. I have the custom object made. How can I this as a feature to the lead and contact detail pages. Please let me know how this is possible

This will act just like any other related list.  See our help docs here on adding a related list to a detail page. 

if you don’t want your tags showing in a table,  you could use a field editor iterating over the model to show multiple tags.  That is explained here.