Lightning Component:

<!--Sample.cmp--> 
<aura:component implements="flexipage:availableForAllPageTypes, force:appHostable">
    <div class="slds-m-around_xx-large">
        <lightning:buttonMenu  iconName="utility:settings" alternativeText="Action" onselect="{!c.handleMenuSelect}">
            <lightning:menuItem label="New" iconName="utility:new" value="new"/>
            <lightning:menuItem label="Edit" iconName="utility:edit" value="edit"/>
            <lightning:menuItem label="Delete" iconName="utility:delete" value="delete"/>
        </lightning:buttonMenu>
    </div>
</aura:component>

Lightning Component JS Controller:

({    
    handleMenuSelect: function(component, event, helper) {
        var selectedMenu = event.detail.menuItem.get("v.value");
        console.log('selectedMenu-' + selectedMenu);
        switch(selectedMenu) {
            case "new":
                //do create
                break;
            case "edit":
                //do edit
                break;
            case "delete":
                //do delete
                break;
        }
    }
})

Output:

Reference: lightning:buttonMenu lightning:menuItem