Modifying an existing node, whether it is an attribute or an element value, can be done by assigning a new value:

[XDocument]$xDocument = @" 
<?xml version="1.0"?> 
<items>   
    <item name='Fridge'> 
        <category>Appliancse</category> 
    </item> 
    <item name='Cooker'> 
        <category>Appliances</category> 
    </item> 
</items> 
"@ 

$xDocument.Element('items'). 
    Elements('item'). 
    Where( { $_.Attribute('name').Value -eq 'Fridge' } ). 
    ForEach( { $_.Element('category').Value = 'Appliances' } ) 

Modifying the value of an attribute uses the same syntax:

[XDocument]$xDocument = @" 
<?xml version="1.0"?> 
<list name='letters'> 
    <name>1</name> 
</list> 
"@
$xDocument.Element('list').Attribute('name').Value = 'numbers' 

If the attribute does not exist, an error will be thrown:

PS> $xDocument.Element('list').Attribute('other').Value = 'numbers' 
 
The property 'Value' cannot be found on this object. Verify that the property exists and can be set. 
At line:1 char:1 
+ $xDocument.Element('list').Attribute('other').Value = 'numbers' 
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
    + CategoryInfo          : InvalidOperation: (:) [], RuntimeException 
    + FullyQualifiedErrorId :PropertyNotFound