Most of the steps pertain to how to back up everything in advance so you dont' forget anything. This is so there are no unpleasant surprises later. In your case however you don't need to do these so after reading over these steps for background you can skip to the step to Boot the installer and start the install.
Be sure to delete all partitions and create a New one for install as shown in Step 7 of
Clean Install Windows 7 which should be your illustrated install guide.
Look on the COA sticker on bottom of PC to see what version it shipped with then download from tutorial Step 1. If its Starter or Basic, download 32 bit Home Premium English SP1 with Media Refresh, unlock all versions by running the
eicfg removal tool on the downloaded ISO, then burn to DVD or write to flash stick using the tool in Step 2. You'll get a menu to select the licensed version.
Follow the steps in the tutorial as they pertain the drivers. Go to the HP Support Downloads webpage at
HP EliteBook 8440p Notebook PC*-* Download drivers and software - specify product name - HP Business Support Center to download the wireless driver to a stick or CD so you can install it if the Win7 installer doesn't provide it. This way you can get online quickly to do your updates which is the first thing to do after install.
Win7 is a driver-complete OS in the installer and quickly updates your drivers when you get online after install and run all rounds of Important and Optional Windows Updates, after enabling
Automatically get recommended drivers and updates for your hardware (Step 3).
I would only import drivers still missing in Device Manager after all Updates are done, or if you still have the place-holder Standard VGA display driver. Don't change out drivers unless performance dictates doing this.