IIS URL Rewrite and Web.config

1) Your existing web.config: you have declared rewrite map .. but have not created any rules that will use it. RewriteMap on its' own does absolutely nothing.

2) Below is how you can do it (it does not utilise rewrite maps -- rules only, which is fine for small amount of rewrites/redirects):

This rule will do SINGLE EXACT rewrite (internal redirect) /page to /page.html. URL in browser will remain unchanged.

<system.webServer>
    <rewrite>
        <rules>
            <rule name="SpecificRewrite" stopProcessing="true">
                <match url="^page$" />
                <action type="Rewrite" url="/page.html" />
            </rule>
        </rules>
    </rewrite>
</system.webServer>

This rule #2 will do the same as above, but will do 301 redirect (Permanent Redirect) where URL will change in browser.

<system.webServer>
    <rewrite>
        <rules>
            <rule name="SpecificRedirect" stopProcessing="true">
                <match url="^page$" />
                <action type="Redirect" url="/page.html" />
            </rule>
        </rules>
    </rewrite>
</system.webServer>

Rule #3 will attempt to execute such rewrite for ANY URL if there are such file with .html extension (i.e. for /page it will check if /page.html exists, and if it does then rewrite occurs):

<system.webServer>
    <rewrite>
        <rules>
            <rule name="DynamicRewrite" stopProcessing="true">
                <match url="(.*)" />
                <conditions>
                    <add input="{REQUEST_FILENAME}\.html" matchType="IsFile" />
                </conditions>
                <action type="Rewrite" url="/{R:1}.html" />
            </rule>
        </rules>
    </rewrite>
</system.webServer>

Just wanted to point out one thing missing in LazyOne's answer (I would have just commented under the answer but don't have enough rep)

In rule #2 for permanent redirect there is thing missing:

redirectType="Permanent"

So rule #2 should look like this:

<system.webServer>
    <rewrite>
        <rules>
            <rule name="SpecificRedirect" stopProcessing="true">
                <match url="^page$" />
                <action type="Redirect" url="/page.html" redirectType="Permanent" />
            </rule>
        </rules>
    </rewrite>
</system.webServer>

Edit

For more information on how to use the URL Rewrite Module see this excellent documentation: URL Rewrite Module Configuration Reference

In response to @kneidels question from the comments; To match the url: topic.php?id=39 something like the following could be used:

<system.webServer>
  <rewrite>
    <rules>
      <rule name="SpecificRedirect" stopProcessing="true">
        <match url="^topic.php$" />
        <conditions logicalGrouping="MatchAll">
          <add input="{QUERY_STRING}" pattern="(?:id)=(\d{2})" />
        </conditions>
        <action type="Redirect" url="/newpage/{C:1}" appendQueryString="false" redirectType="Permanent" />
      </rule>
    </rules>
  </rewrite>
</system.webServer>

This will match topic.php?id=ab where a is any number between 0-9 and b is also any number between 0-9. It will then redirect to /newpage/xy where xy comes from the original url. I have not tested this but it should work.

Just tried this rule, and it worked with GoDaddy hosting since they've already have the Microsoft URL Rewriting module installed for every IIS 7 account.

<rewrite>
  <rules>
    <rule name="enquiry" stopProcessing="true">
      <match url="^enquiry$" />
      <action type="Rewrite" url="/Enquiry.aspx" />
    </rule>
  </rules>
</rewrite>