Create a section called <connectionStrings></connectionStrings>
in your web.config
inside <configuration></configuration>
then add different connection strings to it, for example
<configuration>
<connectionStrings>
<add name="ConnectionStringName" providerName="System.Data.SqlClient" connectionString="Data Source=.\SQLEXPRESS;Initial Catalog=DatabaseName;Integrated Security=True;MultipleActiveResultSets=True"/>
</connectionStrings>
</configuration>
Here's a list of all the different connection string formats https://msdn.microsoft.com/en-us/library/jj653752(v=vs.110).aspx