Help with transferring hard drive to new computer

the funny thing here is that most people would find it much more difficult to pry a HDD out of a laptop and hook it to a desktop (something people don't do often) compared to transferring files between two drives (something many people do several times a day).

At least the hard part is over and done with. Now you simply need to open Windows Explorer (the folder icon on the taskbar in Windows Vista/7/8/8.1, or right click the start menu and select "Open Windows Explorer). I typically open 2 windows, one on the left to display the content I am transferring (the old HDD), and one on the right to display where I want the files to go (Your new HDD). In the left window browse the folders on your old drive until you find the files you want to transfer, and once you find them then navigate the window on the right to the folder you want the files to go to. Once that is done then simply drag the files (or folders) from the left window to the right window and the files will be copied for you.

A few things to take note of:
1) Always copy, do not cut and paste. Copying is a nondestructive process. This way if you put something in the wrong folder, or otherwise make a mistake, you still have your old origanal drive to work from. Dragging and dropping uses a copy/paste option by default.
2) Files transfer, but programs typically dont. Files are things like documents (.doc .docx .txt .rtf), pictures (.jpg .png etc), music (.mp3 .wav .aiff), and movies (.mov .avi .m2t .dv and 100 other extensions), bookmarks, and program specific save files. Most of these files will be found in your "My Documents" folder on a Windows XP machine, or your user profile folders on Vista and newer computers (Documents, Music, Pictures, etc.).
Programs on the other hand make use of the Windows Registry, and while you can copy the files over there is no nice way to copy registry settings, so you would have to go through the entire installation process anyways. Some programs (such as Minecraft) are self contained and do not use the Registry and can be copied from computer to computer, but this is not typical.
3) Once your documents are copied over to your new computer, keep your old HDD in a safe location. An unused HDD can hold information for several years (easily 10+) without issue, so if your new machine were to die then you would still be able to plug the old drive into another replacement and get the data off of it. Also, if you find that you missed an important file, you will be able to plug it in again and find it.
Another option is to reformat the drive after you get all of the data off of it and then use it as a backup drive of your current system. IF YOU DO THIS MAKE SURE TO GET ALL IMPORTANT INFORMATION OFF OF THE DRIVE AS EVERYTHING WILL BE DELETED WHEN YOU FORMAT! Windows Vista, 7 and 8 all have very good backup options built in, and there are several free/cheap backup programs that do a great job of backing up your files. Once a month (or so) plug your old drive into your new computer, run the backup software, and then you will have a safe copy of your files in the event of an emergency.
4) Due to user security issues in NTFS file systems, you may not be able to access all folders on the drive immediately. In a typical setup you will click on a user folder and it will give an error and ask if you would like to take over the permissions for the folders. When you click "Yes" it will seem to not do anything for a while. This is normal, and may take a little while. Note a green bar at the top of the window, and when it clears the width of the window then it will display the contents of the drive. Depending on the age of the drive, and the number of files you have this process can take anywhere from 30 sec to several hours, so just let it take it's time.
5) It may be prudent to do a virus scan on your old drive before transferring documents. Programs like Malwarebytes do a good job at catching potential problems. Even if you do transfer a virus on accident it *should* remain inert for the same reason why copied programs do not work... but better safe than sorry, and there are some pretty sophisticated virii out there.

Hope that helps!