I really wish there was such a thing as easy but having done hundreds of data transfers I can tell you that many situations require different techniques. With that said we tackle the most common ways of getting data from an old or failing computer to a new system.
Deciding on What to Move
This is the best place to start because depending on what needs moved you might be forced to go a certain route.
Common folders like Documents, Images, desktop files, Favorite, Music are very easy to move to a new system. All you would do is just copy from 1 system to another via a network, portable hard drive, cloud storage.
If you require to move certain programs over to the new PC you would have to use a program like Laplink PCMover to do the transfer. Laplink provides software that you install on the old computer and on the new computer as well as a cable (pro version shipped not downloaded). The transfer is relatively easy and you are able to port over many of your old programs.
It is recommended that anything you can install fresh you should install fresh.
State of the Computer
If your computer will not even boot up or the hard disk has errors then you most likely are going to have to remove the hard drive and place it in an external enclosure shell. There are sold at just about all PC repair shops and Ebay, Amazon. They generally run $15 -$30 dollars.
Once you remove your hard drive from the old computer you would place it inside the shells and connect it. Once powered you can connect that hard drive to your new computer and manually browse for files to copy over.
For those who just have a working computer I would probably just transfer the files over a network manually as this requires no extra hardware or software costs. Assuming you already have a router.
Cloud Storage Port
Depending upon the amount of data you have you could take advantage of free cloud storage options like Google Drive or Microsoft OneDrive. Simply install the software on your older computer and tell it which folders and files you want copied over. It may take several hours for the data to fully be copied but you would now have the data stored in the cloud and can easily install that software on your new computer and just copy it all down.
OneDrive gives you 5 GB and Google Drive gives you 15GB for free. You can upgrade to far more space for just a few extra dollars a month. If you do not want a cloud backup of your files you could just cancel the service after the transfer.
An extra advantage of 1 drive paid service is you can get office 365 with 1TB of storage for just $7 bucks a month. That is a lot of space and just about everyone uses Office.
Over Your Network
It’s not hard coping files over to a new computer via your existing home network. You might have to open up sharing permissions but once you are through connecting both computers on the same network it’s just a mater of hunting what you want to copy over. Generally I recommend just dumping everything into the Public folder on the new computer then you can sort and place the files where you want when working on the new system.
Over a External Drive
One super easy way to transfer is just purchasing an external hard drive and plugging in the USB cable to the old system and copying everything you want over to the external drive. From there you just remove it and plug it into the new system and copy over the data you want to the new computer. This is probably the easiest method. You won’t be able to copy over software programs but zero issues with files.
External hard drives can be purchased just about everywhere for a decent price. What is also nice about external drive is you can use them as a backup once the transfer is complete. So it’s not use once and done but you can continue to use the external drive for backup purposes and storage.
Hard Drive is Corrupt
This opens up a whole range of issues. We have a sister site built just for this called http://www.datarecoveryguides.org/ . You can find some really in-depth and geeked out methods that can help you restore corrupt and damaged hard disk drives. Much of it is a little more advanced and generally always will require the purchase of additional hardware and software.