Which HP Pavilion do you have? The Samsung SyncMaster 750s is your monitor. What OS is it running?
Most desktops that came with Windows 95-XP have a few PCI slots inside the box. Computers with Windows 98 (some with Windows 95B) have USB ports. (Older computers may also have ISA slots inside the box.)
If you have a USB port, you can use a USB to ethernet adapter. This will be limited to the speed of your USB (not a good choice if you have USB 1.1). The wired versions are limited to 10/100 Mbs maximum internet speeds. There are some wireless versions as well. See http://www.tigerdirect.com/applications/category/category_slc.asp?CatId=589&name=10-100%20Ethernet%20USB
for examples of wired adapters.
A better choice is the internal one. Again you need to check the specs for your computer and see if there are any available slots and the type on the motherboard. See HP support for the specs of the computer. Slim case formats often have few available slots. (You can usually remove the internal dial-up modem and replace it with the ethernet card.)
These are either wireless and wired. Some run at 1Gbs speed. You will also need a wireless router if you use a wireless card. (A router is a good idea even for a wired ethernet card. It provides protection against some internet problems.) A few PCI wired ethernet are available here: http://www.newegg.com/Store/SubCategory.aspx?SubCategory=27&name=Network-Interface-Cards
. Turn off the computer and unplug the wires to the computer. Open the case, remove the slot cover (or card that you will replace), push the new card into the slot and secure it. Then close the computer and connect your wires. Install the drivers (usually from a CD that will come with the card or by downloading from the manufacturer's site).Then plug an 8-wire RJ-45 cable into the jack and your broadband modem. Then set up following the directions for your ethernet system (dynamic (DHCP) or static IP address, etc). (Wireless networks you install the antenna for the card and then follow the setup instructions for your wireless router. This will include the password.)
I hope this helps.
(the exact setup will depend on the OS - see the control panel Add a network connection)