In Ubuntu Budgie 17.04, you would have noticed that using the GUI Settings - Keyboard - Typing - Switch to Input Source does not respond to a ALT+Shift by itself. You need a third keystroke.
However you can go behind the scenes and install the package dconf-editor and edit one or both of the following keys to get things working:
Go to org.gnome.desktop.wm.keybindings
change switch-input-source to ['<Alt>Shift_L']
Likewise the key switch-input-source-backward change to ['<Shift>Alt_L']
Unfortunately, the Alt+Space behavior is gone and there are no plans to bring it back. Without boring you with details, a ton of things changed 'under the hood' in this upgrade and this feature cannot be easily reimplemented.
There is a project that aims to maintain the old Ubuntu features, the Mutiny environment in Ubuntu MATE. You can even install it without having to completely reinstall your OS, so there is no risk of losing anything.
To install the Mutiny environment, open a terminal and run these commands, the first will prompt for your user password:
sudo apt update
sudo apt install -y ubuntu-mate-desktop
If during the install process, you see a dialog titled 'Configuring lightdm', choose lightdm from the choices.
Now reboot your system and log in.
After logging back in, use the menus in the top left to navigate to:
Preferences -> Look and Feel -> MATE Tweak
Click the Panel tab on the left and switch the first dropdown from 'Traditional' to 'Mutiny'
Now Alt+Space should be working again :)
Feel free to ask if you need help.
Best Answer
You may use (GNOME) Tweaks to achieve your goal. First install it by running
(on Ubuntu 18.04 and later) or
Launch Tweaks and go to Keyboard & Mouse section. Click on the "Additional Layout Options".
A new window should pop up. Look for "Switching to another layout" and expand it. Then check the "Alt+Shift" option.