How do I store a dictionary object in my web.config file?

Why reinvent the wheel? The AppSettings section is designed for exactly the purpose of storing dictionary-like data in your config file.

If you don't want to put too much data in your AppSettings section, you can group your related values into their own section as follows:

<configuration>
  <configSections>
    <section 
      name="MyDictionary" 
      type="System.Configuration.NameValueFileSectionHandler,System, Version=1.0.3300.0, Culture=neutral, PublicKeyToken=b77a5c561934e089" />
  </configSections>

  <MyDictionary>
     <add key="name1" value="value1" />
     <add key="name2" value="value2" />
     <add key="name3" value="value3" />
     <add key="name4" value="value4" />
  </MyDictionary>
</configuration>

You can access elements in this collection using

using System.Collections.Specialized;
using System.Configuration;

public string GetName1()
{
    NameValueCollection section =
        (NameValueCollection)ConfigurationManager.GetSection("MyDictionary");
    return section["name1"];
}

You would need to implement a custom section (See Configuration Section Designer).

What you really want... is something close to this:

<MyDictionary>
  <add name="Something1" value="something else"/>
  <add name="Something2" value="something else"/>
  <add name="Something3" value="something else"/>
</MyDictionary>

Where the XmlAttribute "name" is a Key which it won't allow to have more than one in the code behind. At the same time, make sure that the Collection MyDictionary is also a Dictionary.

You can do all of this with this tool and fill the gap as needed.

I'm not sure how to store a Dictionary directly but you could easily use an array of strings to store a dictionary. For every key, value pair you save out the key as the first string and the value as the second. Then when rebuilding the dictionary you can undo this encoding.

static Dictionary<string,string> ArrayToDictionary(string[] data) {
  var map = new Dictionary<string,string>();
  for ( var i=  0; i < data.Length; i+=2 ) {
    map.Add(data[i], data[i+1]);
  }
  return map;
}