In British English, program is used in reference to computer programs, and programme is used for all other senses of the word. Australian and New Zealand tend to go along with the British distinction, but they are rather loose with it, using program often in all sorts of contexts unrelated to computers. American and Canadian don’t use programme at all. They use program for all senses of the word.
Program is inflected programs, programming, programmer, and programmed. Programme makes programmes, programming, programmer, and programmed.
Examples
For example, these American, Canadian, and Australian publications use program:
Publicly funded programs have enabled 1.2 million more children to gain health insurance since 2008 . . . [Washington Post]
They will try different jobs – and maybe different programs – before settling on one. [The Globe and Mail]
It is concerned about the lack of educational and rehabilitation programs in prisons … [Sydney Morning Herald]
These British publications use programme for all senses of the word unrelated to software:
The Home Office funded-project was set up in April 2007 as part of the government’s wider Prevent counterterrorism programme … [Guardian]
The IMF was on the verge of agreeing a new programme in September to replace a previous $120m facility … [Financial Times]
Over the past few days the programme has been systematically roasted by commentators on all sides. [Telegraph]
And the same publications use program in reference to software:
From here, the attacker downloads a program onto the phone that is able to decrypt passwords held on it … [Guardian]
Another program, Maya, is the de facto tool for computer animation, and is used extensively throughout the film industry. [Financial Times]
The freeware solution is a program suite called Videora Converter. [Telegraph]

