Yes, a lot of this will be obvious stuff to techies, but I've found that if a human asks a techie "I just got a new laptop, can you give me any advice?", the answer frequently will (a) not cover these crucial bases, and/or (b) include a lot of unhelpful stuff to impress the listener. The following is a baseline for what I think a useful answer should consist of. (And if you're the techie, you may want to walk the laptop owner through following these directions, since I'm not actually spelling out what icons you have to click on, etc.)
(1) If you don't want to pay for an anti-virus program, at least install a free one.
Your PC probably came with a trial version of an anti-virus program that will stop working after a month unless you upgrade to the paid version. Of course you can do that if you want. Especially if you ever think you might want phone tech support for your anti-virus software, I expect it's better for a product that you've paid money for.
On the other hand, I know people who thought that if they didn't want to pay for the upgrade to their PC's default anti-virus program, their only option was to let it expire and let their computer run unprotected. If you don't want to pay for a non-free program, install a free one -- Wikipedia has a list of 15 different free or freemium anti-virus products for Windows. PC Magazine gave their "Editor's Choice" award for best free Windows anti-virus to Malwarebytes Anti-Malware 1.70 in 2013 and AVG Anti-Virus Free in 2012, so either of those will work.
(Yes, I know you guys know this. But pass the word on to your Mom or kid brother with the new laptop.)
(2) Save files to a folder that is automatically mirrored to the cloud, for effortless backups.
The era in which everybody talks about backing up, but nobody actually does it, should have ended completely in 2013. Old-style backups, even the incredibly easy options, still mostly required you stop what you were doing for a minute, connect to a remote server or connect a piece of hardware to your computer, and twiddle your thumbs while waiting for some copy process to execute. So nobody bothered.
With cloud-mirrored folders, there's no excuse any more. I found out about Dropbox by asking a mailing list, "I would really like it if there were an online backup service that let me open and close files from a local folder so that there was no delay, but as soon as I made any changes, would automatically be queued to be backed up over the network to a remote host," and my listmates said, "That already exists." Windows 8 comes with the similar SkyDrive service already built in.
You can read a detailed comparison of Dropbox vs. SkyDrive vs. Google Drive, but the key point is to use one of them to mirror one of your local folders to the cloud, and get into the habit of saving stuff to that folder. Obviously this may not apply to you if you have something special going on (if you're creating large multimedia files that won't fit within the several-gigabyte limit imposed by these services, or if your privacy concerns are great enough that you don't want to back up files online), but it's good enough for most people. The horror stories about people saving months or years of writing, and then losing it all in a hard drive crash, should never happen to anyone again.
(3) Create a non-administrator guest account, in case a friend needs to borrow the computer.
Some of my friends and relatives have no problem telling people, "No, I don't care if you need to check the weather, you can't touch my computer!" But if you can't resist the urge to be helpful if someone needs to borrow your laptop for a few minutes, then eventually one of those people will mess it up somehow -- either by installing a game, or visiting a website that installed malware on your computer, or just changing a system setting that you can't figure out how to change back.
When the day comes when someone needs to borrow your computer, you may be too rushed or might not know how to create an unprivileged non-administrator account that they can log in under. So go ahead and do it when your computer is brand new, while the thought is still fresh in your mind. Then if people who borrow your computer sign in under that account, in almost all cases, nothing that they do while logged in should interfere with your user experience when you log them off and log back in as yourself.
That's not a completely secure solution to stop someone from accessing private files on your computer. (There are many pages describing how to boot up a Windows machine from a Linux CD, in order to access files on the computer -- they are usually described as "disaster recovery" options, but they can also be used to access files on a PC without the password.) However, it will stop most casual users from messing up your computer while they borrow it.
(4) Be aware of your computer's System Restore option as a way of fixing mysterious problems that arose recently.
I say "be aware" because, unlike the other three tips, this may not ever be something that you have to actually do. However, intermediate-level computer users just need to understand what it means: to restore your computer's settings and installed programs to a recently saved snapshot, while leaving your saved files untouched. This means if your computer has started acting funny in the last couple of days, you may be able to fix the problem by restoring to a snapshot that was saved before the problems started.
Intermediate users sometimes confuse this with either (a) restoring files from backup, or (b) doing a system recovery (which generally refers to restoring your computer to the state in which it left the factory). So if you're the techie doing the explaining, make sure they understand the difference. (A system recovery will often fix problems, too, but then of course you'll have to re-install all your software; a system restore is more convenient since it only undoes the most recent system changes.)
So these are the first four things I would tell people who were the recipient of a new laptop. What would you tell them?