Installing via terminal is usually using
First of all you need to know what package should be installed, therefor you need to know the package-name.
Assuming you want to install thunderbird you would first of all search for the package name like this
apt search thunderbird
This should output a huge list of packages - locate the proper package ayou are looking for - in our case its simple
Now install the package like this
sudo apt install thunderbird
Finally - i do prefer commandline to install software, but you could as well search for a solution for your base problem - the non working Ubuntu Software application. Therefor it could be helpful to start this software from terminal to get some error-output which could help finding a solution.