when you say PC do you mean that you got a desktop or a laptop? it will work if the connections are both the same, but a laptops HDD is smaller than a desktops, a laptop as a 2.5" HDD and a desktop has a 3.5" so it wont fit into the drive bays, you will need a converter that allows you to do this. If its laptop to laptop as long as you have the same connection it will work, you will have to install new drivers for the laptop you are putting the HDD into but you can get then from the website. I would suggest getting the drivers before you change the HDD over as you may not be able to connect to the internet as you wont have a LAN or WLAN driver.
SpazldNinjaDude is right about drive sizes. If you're putting a 2.5" drive into a tower you will likely have to get a $5 adapter (my tower has slots for 2.5" drives so it's possible that yours does, too).
To elaborate a little on the end of SpazldNinjaDude's post, he means that you will have to reinstall everything on the new drive including the operating system and all of the drivers. However, another choice is to clone the old drive to the new drive. You can do that through several methods - Window's backup is an option and I've used Acronis which works well. Cloning the drive is a good choice if you don't have a backup of the original operating system.