All HP printers with model numbers starting with an "8" have an internal automatic stapling function (with the exception of ML1stFloor-P2 and ML1stFloor-P4).
Internal stapling
To have the printer staple your job automatically using the internal stapler, you'll need to specify your choice in its printing preferences before sending to the printer.
When configuring your print job on your computer, click the link or button for Printing Properties. Note that applications will vary in how this option is displayed (for example, in Office applications it's a "Printer Properties" link just below where you select your printer; in Acrobat Pro and Reader it's a "Properties" button instead). In any case, what you're looking for is the HP driver configuration window with HP logo on it:
Once there, head to the Output tab, and configure your stapling options as desired.
Click OK once finished, and send your job. The printer will staple the finished document for you.
External stapling
If you're stapling a copied document rather than a printed one, you can use the external stapler to staple the copies.
If the printer is sleeping, tap the Home button on the touchscreen to wake it up, and give it a few seconds to do so.
When ready, locate and press the round staple button on the finisher. The button light will illuminate, and then begin flashing, indicating it's ready to receive your document:
While the button is flashing, gently insert your document at an angle into the slot in the finisher below the button, as illustrated in the diagram directly to the right of the button. The 45° angle ensures a perfectly-placed staple every time.
The stapler will sense your document and automatically staple it. Repeat the process to staple additional documents.