The first step would be to watch the device manager screen when you plug in another, different USB device. Do that show up? Where does it show up?
That your com ports aren't immediately visible isn't necessarily a sign for concern. There are tons of things that could cause this most of which are temporary or minor.
Let's go through the list and how to diagnose the issues:
Does fully shutting down and then rebooting the computer change anything? Sometimes immediately after installation things don't show up properly. Try a restart first. There's two ways you should try this. First unplug the arduino, shut down the computer, reboot the computer and then, once you are fully in the OS plug in the arduino. If nothing is different try a slightly different approach. Unplug the arduino, shut down the computer, while the computer is shut down plug in the arduino and then boot up.
Depending on your version of Windows there may be security at that level blocking the installation of the drivers. Typically, when things are working properly, you don't have to go looking for COM ports. Things just magically work. At any point when you plugged in the arduino have you seen a popup in the lower right hand corner of your screen about installing drivers?
Is the arduino plugged directly into a port or are you using a hub? Until everything is working correctly I would recommend plugging directly into a usb port on the computer.
Sometimes windows ports don't play nicely with Arduino. What happens when you plug the device into another port? Try switching between ports.
Confirm that your USB cable is working. What happens if you use that USB cable on another device? Or use a different USB cable to connect the arduino?
DOA Arduinos. What happens when you try to plug the arduino into another computer? I have had, unfortunately, more than a few DOA arduinos. My luck seems to be worse with the minis and micros. As a good initial test for this, when you plug the arduino into a port on your computer does it light up? Does the LED flash?
Unfortunately, right now, we don't have enough information to say "this is your problem." I see that you've posted this question elsewhere(which is good! get some options) but the feedback I see asks for more information. Which is what I'll have to end with. From most 'likely to effect' to 'ehhh... it could be this maybe':
What version of windows do you have?
Which arduino do you have?
Can you plug, for example, a usb thumb drive into that usb port on your computer and get information off of it? Is there a software that pops up when you do this or its it 'just' windows?
Does your computer have a lot of software from the manufacturer installed on it? (These can sometimes cause interesting behavior)
Are you running any Anti Virus?
