The elderly and socially or economically disadvantaged -- who often lack access to the internet or are intimidated by computers -- will be targeted for BCS's 10-week 'e-Citizen' course.
The programme is available through schools, colleges and training centres.
This year marks the deadline for local government to offer public services, such as council tax payments, online; the BCS course teaches consumers how to make online transactions.
"A recent BCS survey revealed that more than a quarter of the UK have no access to a computer, suggesting the IT revolution [has not affected] a significant minority of the population," said BCS chief executive David Clarke.
The PR campaign, which uses 'PC Mouse' as its mascot at local events and was piloted in Swindon this week, rolls out nationally on 14 February with competitions through regional newspapers and radio. Prizes include computers and free internet access.
It will also target lifestyle media for groups that would benefit from the course, such as parents concerned with online safety, the elderly and ethnic minorities.
"There are a number of venues such as public libraries where people can access free internet, but this presumes they know how to use it," said BCS deputy PR manager and press officer Victoria Reinthal.
BCS acts as a trainer and provider of chartered status for IT professionals, but Reinthal said the campaign would boost awareness of its training for the general public.
If you have an opinion on this or any other issue raised on Brand Republic, join the debate in the Forum here.