The goal is to generate the following XML document:

<FruitBasket xmlns="http://www.fruitauthority.fake">
  <Fruit ID="F0001">
    <FruitName>Banana</FruitName>
    <FruitColor>Yellow</FruitColor>
  </Fruit>
  <Fruit ID="F0002">
    <FruitName>Apple</FruitName>
    <FruitColor>Red</FruitColor>
  </Fruit>
</FruitBasket>

Code:

XNamespace xns = "http://www.fruitauthority.fake";
XDeclaration xDeclaration = new XDeclaration("1.0", "utf-8", "yes");
XDocument xDoc = new XDocument(xDeclaration);
XElement xRoot = new XElement(xns + "FruitBasket");
xDoc.Add(xRoot);

XElement xelFruit1 = new XElement(xns + "Fruit");
XAttribute idAttribute1 = new XAttribute("ID", "F0001");
xelFruit1.Add(idAttribute1);
XElement xelFruitName1 = new XElement(xns + "FruitName", "Banana");
XElement xelFruitColor1 = new XElement(xns + "FruitColor", "Yellow");
xelFruit1.Add(xelFruitName1);
xelFruit1.Add(xelFruitColor1);
xRoot.Add(xelFruit1);

XElement xelFruit2 = new XElement(xns + "Fruit");
XAttribute idAttribute2 = new XAttribute("ID", "F0002");
xelFruit2.Add(idAttribute2);
XElement xelFruitName2 = new XElement(xns + "FruitName", "Apple");
XElement xelFruitColor2 = new XElement(xns + "FruitColor", "Red");
xelFruit2.Add(xelFruitName2);
xelFruit2.Add(xelFruitColor2);
xRoot.Add(xelFruit2);

To modify an XML file with XDocument, you load the file into a variable of type XDocument, modify it in memory, then save it, overwriting the original file. A common mistake is to modify the XML in memory and expect the file on disk to change.

Given an XML file:

<?xml version="1.0" encoding="utf-8"?>
<FruitBasket xmlns="http://www.fruitauthority.fake">
  <Fruit>
    <FruitName>Banana</FruitName>
    <FruitColor>Yellow</FruitColor>
  </Fruit>
  <Fruit>
    <FruitName>Apple</FruitName>
    <FruitColor>Red</FruitColor>
  </Fruit>
</FruitBasket>

You want to modify the Banana's color to brown:

1. We need to know the path to the file on disk.
2. One overload of XDocument.Load receives a URI (file path).
3. Since the xml file uses a namespace, we must query with the namespace AND element name.
4. A Linq query utilizing C# 6 syntax to accommodate for the possibility of null values. Every . used in this query has the potential to return a null set if the condition finds no elements. Before C# 6 you would do this in multiple steps, checking for null along the way. The result is the <Fruit> element that contains the Banana. Actually an IEnumerable<XElement>, which is why the next step uses FirstOfDefault().
5. Now we extract the FruitColor element out of the Fruit element we just found. Here we assume there is just one, or we only care about the first one.
6. If it is not null, we set the FruitColor to "Brown".
7. Finally, we save the XDocument, overwriting the original file on disk.

// 1.
string xmlFilePath = "c:\\users\\public\\fruit.xml";

// 2.
XDocument xdoc = XDocument.Load(xmlFilePath);

// 3.
XNamespace ns = "http://www.fruitauthority.fake";

//4. 
var elBanana = xdoc.Descendants()?.
    Elements(ns + "FruitName")?.
    Where(x => x.Value == "Banana")?.
    Ancestors(ns + "Fruit");

// 5.
var elColor = elBanana.Elements(ns + "FruitColor").FirstOrDefault();

// 6.
if (elColor != null)
{
    elColor.Value = "Brown";
}

// 7.
xdoc.Save(xmlFilePath);

The file now looks like this:

<?xml version="1.0" encoding="utf-8"?>
<FruitBasket xmlns="http://www.fruitauthority.fake">
  <Fruit>
    <FruitName>Banana</FruitName>
    <FruitColor>Brown</FruitColor>
  </Fruit>
  <Fruit>
    <FruitName>Apple</FruitName>
    <FruitColor>Red</FruitColor>
  </Fruit>
</FruitBasket>

Goal:

<FruitBasket xmlns="http://www.fruitauthority.fake">
  <Fruit>
    <FruitName>Banana</FruitName>
    <FruitColor>Yellow</FruitColor>
  </Fruit>
  <Fruit>
    <FruitName>Apple</FruitName>
    <FruitColor>Red</FruitColor>
  </Fruit>
</FruitBasket>

Code:

XNamespace xns = "http://www.fruitauthority.fake";
XDocument xDoc = 
    new XDocument(new XDeclaration("1.0", "utf-8", "yes"),
        new XElement(xns + "FruitBasket",
            new XElement(xns + "Fruit",
                new XElement(xns + "FruitName", "Banana"),
                new XElement(xns + "FruitColor", "Yellow")),
            new XElement(xns + "Fruit",
                new XElement(xns + "FruitName", "Apple"),
                new XElement(xns + "FruitColor", "Red"))
                ));