Consider the type of word you are working with. Adverbs can be used to enhance actions, places, and times. For instance, the word "ran" is an action.
Think about the different ways in which you can perform the action mentioned in the word. Keeping the example of the word, "ran," you should be able to think of several ways in which a person can run. Some examples of how a person can run include slowly, quickly, clumsily, or gracefully.
Find the word that best suits your situation. If your protagonist is running quickly, start with the word "quickly."
Look up the adverb you have selected in your thesaurus to see if there are any adverbs you find more appealing. Listings for "quickly" include briskly, hurriedly, hastily, swiftly, and speedily.