It looks like you're making a login script, but it's not really doing anything. Inside the count if, you should be assigning variables - not just stating them randomly. It should be $_SESSION['username'] = $variable etc. You really should know how variables work if you're attempting programming.
Also, you don't need encapsulation when echo'ing variables in PHP. echo $name; will work just fine. Using encapsulation ("'s) like you're doing will also work, but takes longer as php takes it as a string, then parses the value for $name inside the string. While you're learning, you should note the difference between ' and ". Encapsulating text in ' will tell php to treat it as plain text, whereas encapsulating a string in " will tell php to parse any variables inside it as their value.
An example of that:
$foo = 'bar';
echo $foo; // Will echo bar;
echo '$foo'; // Will echo $foo;
echo "$foo"; // Will echo bar;
Also, look at the isset() and empty() functions for things like session vars.