Not only must you avoid any processor-intensive work such as editing, don't even check your emails or browse Facebook. NOTHING. Allow your computer to concentrate solely on the most important task in the world right at that moment - getting your files safely onto your hard drive.
Likewise, when you're backing up your photos to your external drives, or your cloud, or wherever. Those periods of transfer are SO critical. If any interruption causes corruption to your files, you might not find out until much later, after you no longer have the original files to fall back on.
Some of you will think that I'm making an unnecessarily big deal about this. Many of you, in fact, will profess to frequently browsing the web while copying files, and you'll boast that you've never had corruption. That doesn't mean you're smart, or invincible, it means you're LUCKY. And luck always runs out, eventually. When you are mourning the loss of some important photos, believe me, catching up on your friends' news won't seem that important after all.
There's a very important aspect to this which I must discuss. Many times on forums people post that they've found a corrupted file or files in their set. Many other people are very quick to say "Oh, your card is corrupted, get a new one."
I've often wondered how many perfectly good cards have been discarded for no reason. You see, if you find a corrupted file on your computer, there's a very good chance that the corruption happened during the transfer, because you couldn't leave your computer alone for a few minutes. There's a very good chance that the file on the card was perfectly fine.
So in these online discussions, my first question to the poster is always "Do you still have the files on the card?" If we're lucky, they still do; in which case they can try copying them across again, and checking if the corruption is still present. Quite often, I'm pleased to say, it's not. This is a great outcome - we've got the photo back, and a card wasn't victimised and discarded unnecessarily.
But sadly, often the poster has already formatted the card, and used it again. This sucks, because then we don't know, you see? We don't know if the problem was the transfer, or if the card itself is truly faulty. That, of course, means people remain nervous every time they use that card in the future.
So leave your computer alone while files are transferring. Just chill out. Make a cup of tea or something. Don't risk it.
In addition to this, of course observe normal computing common sense. Shut it down or restart it regularly. Keep the hard drive at least 1/3rd empty at all times. And run maintenance software regularly (see the bottom of this page).
*Please don't use a cable. Always a card reader.