Geany actually has the options that you're looking for built in.
At the top of the screen towards the middle there is a button that looks like a little gear, as well as a button that looks like a brick wall. These are your options for compile and run. Once you've written your code to your satisfaction, you simply click the compile button, and at the bottom of your screen you'll see the output, and if there are any compile time errors. Once complete (assuming no errors) clicking run will cause Geany to open your system's default terminal and execute the program. The terminal will show exit status code when complete and will remain open until you close it.
As for compilers, most major distributions of linux have a pre-packaged collection of compilers and linkers. For ubuntu I believe you would go to the terminal and type the following:
sudo apt-get update
sudo apt-get install build-essential
These two commands will update the list of packages on your system, and then install the essential libraries, headers, and compilers needed for C, C++, and other common programming languages.
Best of luck in your endeavors.