The obvious way to quiet a hard drive is to replace it with an SSD. Not only do they run quieter, but they provide faster data access.

Fred mentioned the keyboard as a possible source of noise. I’m not sure how you can reduce keyboard noise without going to a touch screen. Most laptop built-in keyboards are about as quiet as any keyboard. However, there is a really good reason to use an external keyboard with your laptop – you reduce/eliminate wear and tear on the built-in keyboard. The built-in keyboard will last a lot longer if you use an external keyboard as much as possible.

A noisy HDD could be one answer. Loose things that are vibrating could be another. That merely takes a bit of tapping and feeling to find out what it is.

I’d offer another choice, a noisy fan. Then can run fast, vibrate if they’re loose, even make a noise if a chunk of dust or even a little debris has found it’s way into the case.

Protect and clean the vents, that has always been the source of my noises, especially if the laptop gets heated and the fan runs on high speed for a while.

I do a lot of service work. The most common cause of noise from a laptop is usually caused by the user. Most laptops have vents in the bottom that allow air to be pulled in. When you keep a laptop on a soft surface, the vents are blocked. That causes temperatures to go up because not enough air is moving through the system. The system is designed to protect itself from over-heating and to do that it speeds up the fan in order to get more air moving. Those higher speeds are the source of the noise.

In most cases, simply placing the laptop on a hard surface will solve the problem if you wait a bit while it cools down.

Well the noisy HDD has been solved by @mrjimphelps not only the noise factor but the performance factor will make an extremely pleasurable fix for that problem.
Noisy DVD/CDROM (my old Laptop here sounds like a washing Machine spinning up) drive tricky that one if its a favourite Movie, Music, game or even install disk consider copying to a file/folder or USB stick Rufus etc (if so equipped + space permitting) even for installs.
Noisy CPU fan consider switching to Passive Cooling in advanced power options although if your a gamer/heavy CPU user you’ll have to weigh noise for cooling against Chip longevity although shouldn’t be much of a problem.
External (none CPU) don’t take your Laptop to bed, yes I know it shows it on the Movies and Ads, because there be the infamous Dust Bunny’s. For cleaning you can go with the Compressed air can, pricey and a bit harsh if you go at it Gung Ho Vacuum cleaner with attachment works although please don’t Jam it in there, more a safe distance otherwise you’ll do more harm than good around the exterior vents 🙁
Top and bottom of it all noise is fairly good, just like a car when you turn a key it speaks to you (no I aint lost it, hearing things lol 😉 ) if it makes a noise that its never has before worth an investigation obviously and then again some are just naturally noisy and nothing to worry about but as Fred, rightly, says if there’s a grinding from the HDD time to Back up and treat your self to a shiny new SSD you’ll love it, and if your under the hood of your Laptop blow a few of those Cob Webs away while your there, your machine will love you for it 😉

I miss the rattling of ol’days hard drives. That sound meant activity. In nowadays computers, you have no idea of what’s going on there, some don’t even ship a drive activity LED.

Regarding fans or speakers, my new laptop makes some subtle white noise that was enough to disturb me. And I cannot open it to figure it out due to warranty voiding stickers. It seems to be a metal case totally passive laptop with a low-power (yet incredibly efficient!) Celeron CPU. I honestly don’t know if this is fan activity – and that’s really quiet for a fan – or some hardware interference noise coming out of the speakers that last some seconds, even if the sound is muted  – and this is OS agnostic.

Lose screws can also add vibration to the case joints as the computer becomes old – especially old computers that had hot CPUs and power supplies that caused materials to expand and contract a lot of times every day over the years. And that can feedback into itself to the point of some screws unscrew themselves out of vibration to the point of falling off. Here, some soft screw glue can get’em tight yet make it possible to drive them out should one need it.

Modern OSs make a good job of managing power. Windows can do ‘stuff’, and on Linux you can manage hard drives speed and spin down time, and also the CPU max frequency and selecting an appropriate governor. That maximizes battery life while having enough power to do your job without noticing a loss of significant performance.