How to declare multiple connections in a webpage and call them when needed

If the connections are all for the same database, same credentials, then there is no point in doing this, simply create the connection as and when you need it, then use it. If the connections require difference connection strings then create an entry in the web.config for each string

<configuration>
  <connectionStrings>
    <add name="Conn1" connectionString="server=a;database=b;Integrated Security=true"/>
    <add name="Conn2" connectionString="server=c;database=d;username=blah;password=mypassword;"/>
  </connectionStrings>

Then read them via ConfigurationManager when you need them

SqlConnection con = new SqlConnection(System.Configuration.ConfigurationManager.ConnectionStrings["conn1"].ConnectionString);

If you're wanting to create SqlConnection objects and kept them between page requests etc then don't do this, it is bad for performance and resource use, let ado.net handle the connections and connection pooling for you by simply creating connections when you need them. Google "ado.net connection pooling" if you want to learn more.