If your computer came with a serial port built into it (pretty rare these days), go to the support site of your computer's manufacturer, enter the identifying information about your specific model (probably the serial number), and look for the driver for the serial port.
If you have difficulty doing the above, please provide the make and model of your computer (and its serial number).
If you installed an add-on PCI card for the serial port, what is the make and model of that PCI card?
Otherwise, right-click on that entry in Device Manager and select the "Details" tab.
Select "Hardware Ids" in the drop-down list under "Property"
Copy the first line in the "Values" box and paste into a Google search.
If you get no hits when searching for the entire first line, search only for the VEN/DEV information.
Using the screenshot below as an example:
Search for PCI\VEN_14F1&DEV_10B4&SUBSYS_9300141D&REV_89
If no hits, search for PCI\VEN_14F1&DEV_10B4
Alternatively, you can use one of these PCI VEN/DEV databases:
Once you know the manufacturer and model of the serial port, you should be able to find the driver for it. If at all possible, avoid third-party driver download sites. Look for the website of the device manufacturer.