In the simplest case:
You start by finding yourself a good editor. This can be an editor that runs on your own computer, or you can use one of the many editors that are supplied in the shell as part of your DreamHost account. If you use editor that runs on your own computer, it is helpful if you select one that allows you to save your files with "unix- style line endings".
PHP code is created in an editor and saved as a file. Name the file "something.php" and place that file in a web-accessible directory of your domain. If you created the file on the server in the shell, you can just create it in the appropriate place; if you created it on your own computer, you will need to to transfer it via an FTP program to the appropriate place on your web server. From the information you gave above, that would be in the "myhomebuiltplane.com" directory of your DreamHost account space (or a directory beneath that).
Assuming you now have simple.php" in your user directory "myhomebuiltplane.com" (which is in the files system at DreamHost as /home/yourusername/myhomebuiltplane.com/), you execute the PHP code by browsing with a web browser to "http://myhombuiltplane.com/simple.php".
When you do this, the PHP code in that file will be executed (the php statements in the file you saved will be read and actions taken) and, depending upon what those statements were, output will be sent to the browser, data may be added to the database, files may be created/deleted, and so on ...
That's the basic idea!