$secretNumber = 5;

What you want to do now is compare the player's guess with the secret number, and tell them if they guessed correctly. To compare one value to another and get a true or false result, you use two equals signs (==). If the values on either side are the same, then the result is true; otherwise, it's false.
Here's how you'd check the player's answer in your PHP:

 if($secretNumber==$playerGuess){
     echo("<br />That's right! I was thinking of {$secretNumber}!");
 }

Add this code in (after those variables' values are set!) and then run the program. Try guessing correctly (i.e. 5) and incorrectly.

Have you noticed a few issues with what's happening here? For one thing, the player is still asked to pick a number even when they've won the game! You can fix that, though, by using else statements, after your if statements. You can't use else on its own, it only runs the code inside it if the test on the if statement just before it was false.
So, to only show the form for the next guess if the player has not yet guessed the secret number, you need to add an else on to your if from above and move all the form code into it, like this:

 if($secretNumber==$playerGuess){
 echo("<br />That's right! I was thinking of {$secretNumber}!");
 }
 else{
     echo "<form method='get'>";
     echo "Your guess: <input type='text' name='guess'/>";
     echo "</form>";   
 }