For free advertising space, many publications will write an article about you or your product if you purchase advertising space with them. One way publications sell advertising space is to agree that if the advertiser purchases the ad, he will also receive a certain amount of free editorial space. This free editorial space essentially doubles the amount of space you get for a given amount of money. This editorial space is devoted to an article about the company or individual or product, and it has the added cachet of seeming to be work of an outside source. The editorial company be written by the publication staff, or the advertiser may provide the copy.
Press releases can be another excellent source of free space.
A well-written press release on an interesting subject will attract the editor's interest. The editor may even follow up with a phone call for more details. The result can be anything from a paragraph to a feature article. All this comes for the price of mailing the release. Keep in mind that you want to target the publication that write about the kinds of things you are doing.