In Salesforce Visualforce Page, we can get and set localStorage using JavaScript localStorage.setItem() and logcalStorage.getItem() methods.

Sample Visualforce Page Code:

<apex:page>
    <div id="txt">        
    </div>
    <script>
        localStorage.setItem( 
            'exampleItem', 
            'Testing' 
        );
        console.log( 
            'exampleItem is', 
            localStorage.getItem( 'exampleItem' ) 
        );    
    	document.getElementById( "txt" ).innerHTML = localStorage.getItem( 'exampleItem' );
    </script>
</apex:page>

Output: