1) The connection string
ConnectionString is a string that contains information about how to connect to the database. It typically includes the database location, the database name, database user credential information (user name, password, and type of authentication to use to authenticate the user). The connection string is going to vary between the type of database that you are connecting to. Since it contains sensitive information about your database you should take care in protecting this information by storing it in your web.config file and then encrypting the connection strings section.
2)? What do you mean what are the steps? A connection string is simply a String that contains information about the database. It can be used with .NET classes and controls to open a connection to the database so that you can run queries on the database. Please review the following articles that outline how to use a database:
Database tutorial Part 1 Database tutorial Part 2
3) Not sure what connecting to a database has to do with installation/setup applications. You should probably consider implementing your application first and then create your installation/setup application.
4) If you are developing an ASP.NET application, then you need to have the .NET Framework installed on the computer that will be hosting the application. The version of the .NET Framework that you software requires is going to depend on the version that you have selected to target and the version of Visual Studio that you are using.
As for a database suggestion: MS SQL requires you to purchase the software and a license to use it. This can be quite costly but has many benefits regarding security features etc that you may be interested in.
MySQL is a free database management system available that you can use...
You really should do research into the types of databases available to find the one that best suits your software requirement needs.
-Frinny