There are two main ways to open a PHP code island (to enter PHP parsing mode), and you are welcome to choose which you prefer. The most common (and recommended) manner is to use <?php to enter PHP mode, and ?> to leave PHP mode, however you can also use the short tags version, <? and ?>.
The short version has one big advantage and one big disadvantage. The advantage is that you can output information from your script by using a special short tags hack, <?=. Here is how that looks:
Here is the equivalent written using the standard open and closing tags:
<?php print"Hello, world!"; ?>
As you can see, the short tags version is much shorter, if a little harder to read. However, the big downside to the short version is that it clashes with XML, which also uses <? to open code blocks. This means that if you try to use XML and short-tagged PHP together, you'll almost certainly encounter problems - this is the primary reason people recommend using the normal open and close tags.
You can switch into and out of PHP mode by using <?php and ?> whenever you want to and as often as you want to.