How can I record my screen?
gtk-recordmydesktop 
Adds an easy to use graphical icon on the GNOME toolbar to make a pleasure use and configure the audio and video capture and screencast application recordMyDesktop.
As mentioned at 20.04: Can't install gtk-recordmydesktop and on the package search, the package is not available on the main repository anymore, and sudo apt install gtk-recordmydesktop fails. I'm not sure why the http://apt.ubuntu.com/p/gtk-recordmydesktop link seems to work, maybe it installs an older version. But this indicates that the software is not being actively supported.
recordmydesktop
This is the non-GUI backend of recordmydesktop, and it is still available in 20.04:
sudo apt install recordmydesktop
recordmydesktop --on-the-fly-encoding
This will record until you stop the program on the terminal e.g. with Ctrl + C.
--on-the-fly-encoding encodes the output immediately; without it you need to wait for a possibly long time at the end for the encoding to be done. I haven't seen any significant downsides to that option yet, likely it will just take a bit more of CPU resources, but it is generally worth it.
It should be able to do everything that gtk-recordmydesktop does, but it is a bit harder to learn as you have to deal with the command lines.
You can set a stop recording shortcut e.g. with:
recordmydesktop --stop-shortcut=Control+s
You can select to record a single window as shown at: How can I get the value of Window ID?
recordmydesktop --windowid `xwininfo | grep 'id: 0x' | grep -Eo '0x[a-z0-9]+'`
This will allow you to first select the window with a mouse click, and it starts recording after you click.
How to record sound output with it: https://unix.stackexchange.com/questions/3490/how-can-i-record-the-sound-output-with-gtk-recordmydesktop
xvidcap (no longer maintained, package is no longer available)
A screen capture enabling you to capture videos off your X-Window desktop for illustration or documentation purposes. It is intended to be a standards-based alternative to tools like Lotus ScreenCam.
Video can be saved in MPEG or AVI files format.
I like Byzanz; it records your activity as a GIF file.
It's pretty light and works well, especially for putting a shorter screencast on a webpage or in an email.
You can either get it from the PPA (might have a more up-to-date package but is 'unsupported'):
sudo add-apt-repository ppa:fossfreedom/byzanz
sudo apt-get update && sudo apt-get install byzanz
Or you can get it from the official Ubuntu repositories by clicking the button below:
For further information:
How to create animated GIF images of a screencast?
Kazam
It's a good application for this purpose:
Home, install, or simply sudo apt install kazam
It gives you a delay before recording. Recording is done in HD and the output is in .mkv format which is accepted for YouTube so there is no need to convert and re-render.
There are some useful keyboard shortcuts too:
To start the recording: Super + Ctrl + R
To pause the recording: Super + Ctrl + P
To stop the recording: Super + Ctrl + F
To show/hide main window: Super + Ctrl + W
On Ubuntu 20.04 I met this bug with it where the video is not captured/or is all black: https://github.com/hzbd/kazam/issues/9 even though recordmydesktop video capture worked on the same machine.