This is the adverb form: it describes HOW something is done, namely in a way that gets a good result for the money spent. You attach it to a verb — 'produce it cost-effectively', 'deliver the service cost-effectively', 'heat the building cost-effectively'. The meaning is the same as 'cost-effective', with the same warning attached: it is not a synonym for 'cheaply'. Doing something cheaply just means spending little; doing it cost-effectively means the spending was well matched to what came out of it. It is a heavy, formal word that lives in reports, tenders, and management writing, and it usually sits at the end of a clause. In practice you will meet the adjective 'cost-effective' ten times for every one 'cost-effectively', and many careful writers rewrite the adverb away — 'in a cost-effective way' — because the four-syllable ending is a mouthful.