How much does it cost to run a sales promotion?
If I did it mainly online, how much would I expect to pay (roughly)?
Can you provide more information on what you are looking to do and on what scale?
There are many ways to promote online however it comes down to scale and target market. Some markets can be costly to promote to depending on the method used. You can promote for free online however without knowing what type of promotion you are looking to do it is hard to answer this one.
Adwords: Cost depends on the keyword value however you control the budget.
Facebook: You can control the cost.
Email marketing: I wouldn't send emails from your address, I would use a third party for that as bulk emails can ruin your email rep.
Those are the most common however really comes down to you and your budget vs the target market. In some cases it would be more productive to try direct marketing instead of casting a net (adwords etc). Casting is very popular and you can get good ROI however direct marketing tends to bring in much better results.
Either way you control the budget so it would be an idea to work out how much you want to spend then look at what can be done for that price.