Add a unique id to each submit button:
<input type="submit" name="submit[1]" value="Submit">
<input type="submit" name="submit[2]" value="Submit">
<input type="submit" name="submit[3]" value="Submit">
Then you grab the id from $_POST or $_GET. For example:
Array
(
[submit] => Array
(
[3] => Submit
)
)
Edit:
Take this concept - HTML form elements to PHP arrays - and apply it to the other elements.
<table>
<tr>
<th>Program</th>
<th>Department</th>
<th></th>
</tr>
<tr>
<td><input type="text" name="program[1]" value=""></td>
<td><input type="text" name="department[1]" value=""></td>
<td>
<input type="submit" name="edit[1]" value="Edit">
<input type="submit" name="delete[1]" value="Delete">
</td>
</tr>
<tr>
<td><input type="text" name="program[2]" value=""></td>
<td><input type="text" name="department[2]" value=""></td>
<td>
<input type="submit" name="edit[2]" value="Edit">
<input type="submit" name="delete[2]" value="Delete">
</td>
<tr>
<td><input type="text" name="program[3]" value=""></td>
<td><input type="text" name="department[3]" value=""></td>
<td>
<input type="submit" name="edit[3]" value="Edit">
<input type="submit" name="delete[3]" value="Delete">
</td>
</tr>
</table>
Again: use the unique IDs to set each row's form elements apart.
Here's one method for grabbing the data in PHP. Obviously you need to get the ID from the submit button and then use that ID to reference elements in the $_POST or $_GET array.
if ( isset($_POST['edit']) && is_array($_POST['edit']) ) {
$key = key($_POST['edit']);
$program = $_POST['program'][$key];
$department = $_POST['department'][$key];
}