SPSecurityTrimmedControl is a useful SharePoint control to control the visibility of content and controls on your site. In order to use this control, simply add the following code into your page:

<SharePoint:SPSecurityTrimmedControl runat="server" PermissionsString="ManageLists">
Your code here.
</SharePoint:SPSecurityTrimmedControl>

1. Create a project (It seems .net 4 doesn't work well with SharePoint 2007)
2. Add the reference to Microsoft.Office.Server.dll. (C:\Program Files\Common Files\Microsoft Shared\web server extensions\12\ISAPI)
3. The log code looks like this.

try
{
  throw new Exception("This is a test");
}
catch (Exception ex)
{
  Microsoft.Office.Server.Diagnostics.PortalLog.LogString(ex.Message, null);
}

Done

I find this Post from Dave Wollerman's blog. I think it is very useful to me. Here is the link SharePoint 2007 Single Sign-On Setup

Here is the step you need to do in order to config your SharePoint site using form authentication.

Preparation: You should have a existing ASP.net 2.0 membership database. Here is the link about how to create this database.
There is a existing user testAdmin already created in the membership database.
SQLConnectString in web.config:
<connectionStrings>
<add name="ApplicationServices"  connectionString="Data Source=localhost;User ID=sqluser;Password=Password1;persist security info=False;initial catalog=DemoUser;"  providerName="System.Data.SqlClient" />
</connectionStrings>

Membership Configuration Section in web.config:
<membership>
  <providers>
 <clear/>
 <add name="AspNetSqlMembershipProvider" type="System.Web.Security.SqlMembershipProvider" connectionStringName="ApplicationServices"
  enablePasswordRetrieval="false" enablePasswordReset="true" requiresQuestionAndAnswer="false" requiresUniqueEmail="false"
  maxInvalidPasswordAttempts="5" minRequiredPasswordLength="6" minRequiredNonalphanumericCharacters="0" passwordAttemptWindow="10"
  applicationName="/" />
  </providers>
</membership>

Step 1. Create a web application and a site collection.

1. Open the SharePoint Central Administration site.
2. Click Application Management tab.
3. Click Create or extend Web application
4. Click Create a new Web Application
5. In the Port textbox, put the port number you want. I am going to use Port 112 in this example.
6. Under "Allow anonymous", Click "Yes".
7. Click Ok.
8. After you get the information says the web application has been successfully create. Click the "Create Site Collection". I am going to create a publishing portal in this example. 
9. Enter the site title. For site template, select the "Publishing Portal" under the Publishing tab.
10. Click Ok.

Step 2. 
1. Open the site we just create. In this example it will be http://localhost:112. 
2. Click the "Enable anonymous access" link in my front page.

3. Click "Entire Web Site".

Step 3. Change the SharePoint authentication method
1. Open the SharePoint Central Administration Site.
2. Click the "Application Management" Tab.
3. Click the "Authentication Providers" under the "Application Security" section.

4. Confirm the web application you want to modify is correct. In this case http://localhost:112
5. Click the Default
6. Change the Authentication Type to "Forms"
7. Set the Membership Provider Name to "AspNetSqlMembershipProvider"
8. Set the Role Manager Name to "AspNetSqlRoleProvider"

9. Click Save.

Step 4 This is step is optional. You only need to do this if you want to set users from your membership database as your site collection administrators.
1. Open the web.config file for your Central Administration. The file is located in "C:\Inetpub\wwwroot\wss\VirtualDirectories\PortNumber" - PortNumber is the port number for your Central Administration site.
2. Add the SQLConnectString and Membership Configuration Section in the web.config.
3. Save and close your web.config file.
4. Open the SharePoint Central Administration Site.
5. Click the "Application Management" Tab.
6. Click "Site Collection Administrators" under the "SharePoint Site Management" Section.
7. Confirm the site collection you want to modify is correct. In this case http://localhost:112
8. For primary site collection administrator type "test" and verify user.  It may take a few seconds, but the page should underline the text in the textbox indicating that the username is valid.
9. Click Ok.

Now if you open the SharePoint site, you should able to see a "Sign In" link at the top of you screen.

Click that link you will able to see your login screen.

Then the screen should look like this. If you configure the step 4, you should be able to see the "Site Actions" menus as well.

Aspnet_regsql.exe is a tool for installing the SQL Server database used by the SQL Server providers. The file is located in the "c:\WINDOWS\Microsoft.NET\Framework\versionNumber folder" on your web server. There are too ways to run this tool: the wizard form and the command line.

1. To run this using wizard is very simple. 
Step 1: Run the aspnet_regsql.exe from your command line without any arguments. Then the wizard windows form will appear.  Click the Next Button.

Step 2: Choose what you want to do with the sql database. In this example we want to create a new application services database. So we just select the first option then Click the Next Button.

Step 3: Enter your sql server name, authentication method and the database name. If the database has already existed, you can select the dropdownlist. If the database is new, you only need to type in the new database name in the dropdownlist. Click the Next Button.

Step 4: Confirm the information then then Click the Next Button.

Step 5: Done. 

After that your database should be created. And it should look likes this.

2. Also you can run the tool as a command-line utility. The options for the command are

So if you want to add database elements for membership and role management in database test on localhost using the current windows user. The command should be:

aspnet_regsql.exe -E -S localhost -d test -A mr