Is your old computer operable? Does it boot into the operating system? If you answered yes to both, then data can be transferred by attaching an external hard drive and doing a direct file copy to it. If you answered no, then the data migration process requires that your old hard drive be removed and installed on a computer that does boot up. From there, files can be copied to another hard drive.
If it can't, setup the old drive as an external drive so files can be copied to another drive.
Which folders do you want transferred? Pictures, videos, documents, music, applications, settings? Transfer them onto an external drive or directly on the new drive if possible.
Make sure all of the files and folders transferred properly. This is done by comparing file sizes. Also spot check by opening random files in different folders.