basics to know
Not every device or every application you may want to document is created equal.
When screen recording, the quality of the recording will depend on a number of factors, the most important being the processing power of the device making the recording.
As in most cases, the computer or phone you are using is having to do all the work of running the source of your visuals while also recording it in real time.
As such if you have a computer or phone that struggles to run multiple apps at a single time, the recordings it will produce will likely be low fidelity.
That is not saying that you shouldn't try screen recording on a computer that isn't state of the art, but just to set your expectations accordingly.
When recording source footage, whether it be for documentation, research-creation, use in a presentation, etc. it is worth knowing that not all app makers or services want or intend for you to record their apps.
On mobile devices this can commonly exhibit as the sound output being blocked by the recording or very low framerates if the app is just not well optimized.
On computers this can be a literal black box where an app or window was present in the recording.
While there are often workarounds for technical issues, these instructions center on workflows that do not require additional equipment for the screen recording process.
on an Apple Computer
No matter what you use you will need an extra program to help you record system sound.
Quicktime Screen Recording
By default this is the simplest way to record your screen on a Mac. The downside is that it can also be unreliable, as even on a professional workstation, this form of recording sets it's own quality. So while worth trying, it will not work for all purposes.
IMPORTANT: Audio Workarounds
One thing that the Mac OS will not let you do by itself is record the sound output of your computer, at least not by default.
To this end there are multiple free or open source audio re-routing programs that exist that allow you to overcome this hurdle.
If you have a Mac with an OS more recent than OS Catalina, Blackhole is a popular solution. (Installation and configuration shown in both the youtube tutorials here.)
If you have a mac running Catalina or older iShowU Audio Capture functions identically, but was designed for those systems. (So after completing installation, you could follow all the steps associated with Blackhole in that video.)
While this is a bit more technical than most Mac users are used to, it's by no means beyond the average user to get working.
Alternative: OBS Studio
If you are willing to put in a little bit more work than Quicktime, Open Broadcaster Software is an amazing open source piece of software, used by most live streamers, that will give you far more control and the ability to composite live (if you're interested and if your computer can handle that.)
The main advantage of OBS over Quicktime is that OBS will auto configure in order to find a more stable quality level and framerate for your recordings, rather than having the framerate dive like you can commonly see with Quicktime.
The tutorial linked here deals with adding both a display capture and a webcam capture, but you can omit the webcam if you do not need it.
with an iPhone
Screen recording an iOS device has gotten significantly easier with the iOS 15 update.
Screen Record (iOS Built-In App)
In one of the recent iOS updates, Apple uncrippled it's built in screen recorder on iOS by allowing it to record the system sound of the device and not just the internal microphone. This is done easily with Screen Recording feature accessible from the control center menu. You can check out this YouTube tutorial for step by step instructions.
Alternative: Tether to Quicktime
The best way to record iOS apps on older iPhones (iOS 8 or later) is to "tether" the phone to your mac. This is done by connecting to your mac via USB, opening Quicktime and recording your phone through the Quicktime App. Note that you must select "Trust this computer" or your phone will not be accessible. You can check out the youtube tutorial to the right for more information.
with an Android Device
Screen recording an Android Device is relatively easy with the built-in functions of the device as well as with a free app.
Screen Record (Android Built-In App)
As of at least Android 11, the built in screen recorder for Android does everything you need it to do. It will allow you to record your phone’s screen along with your choice of audio (silent, media sounds only, media sounds and voice notes.)
If for some reason you cannot access Screen Record on your phone, the free version of the app XRecorder is a possible alternative. The app gives you significantly more control then the built-in app, but is also a bit less user friendly as a result, you can check out more information on it in this youtube video.
Swipe down from the top of your screen (revealing the Quick Settings Menu).