You have this controller: Intel® 82579LM Gigabit Ethernet PHY Specifications
It is a "wired" controller as you already know.
You need to purchase a wireless LAN (NIC) controller. You need to determine what slots are available on your motherboard and purchase a controller for one of those slots, or get an adapter that can use a USB port. You can find many wLAN adapters that will fit PCI Express slots, PCI slots, USB ports, etc at this link (as an example) Wireless Adapters, PCI Adapter, Wireless-G Adapter - Newegg
To provide you with better information, tell us what motherboard (model number) and slots you have available, what OS you are using, and what wireless network you want to connect to (B, G N, AC, etc).
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What is important, and I am glad you provided the model number of the PC, is that you need a "low-profile" card.
Look under "slots" here: HP Support document - HP Support Center
So, the card I gave as an example is provided with a full height bracket, and a low profile bracket. If you were to purchase such a card, you would have to remove the full height bracket and add the low profile bracket. This is usually one or two screws, and is not an issue.
This card, as an example, will support most all of your wireless network needs.
Note: there are cheaper cards. This one is not bad. Just remember that you need a PCIe x1 card with a low profile bracket, and antennas. Some antennas attach directly to the card, some have a wire that is attached allowing you to put the antenna in a "good" location.
Usually, once a card like this is installed (and antennas attached), and the PC turned on, the OS will detect the card and install the drivers needed. Then, you just connect to the network you want.
Also, depending on your needs, a WLAN USB option is always there as well.
Good luck with the install.
This message was posted on behalf of Intel Corporation
In addition to the previous recommendations, we would like to mention wireless adapters (PCIe Add-in cards) from Intel®:
Both have models that include Low profile and full height brackets. You may be able to find these at your preferred retailers or Intel® Technology Providers.