Examine the sentences you want to convert and decide which initial sound to use for the alliteration. If you are trying to add dramatic affect, there may be a particular sound that is most appropriate. For example, if you are writing about a snake, a "s" sound would be an obvious choice for the alliteration. In a long-form text, using the same alliterative sound for the entire text might be difficult, so you might want to switch sounds after each sentence.
Exchange words in the original sentence for synonyms that begin with, or at least contain, the sound you wish to use for the alliteration. Use a thesaurus to find ideas of words to use as substitutes. You do not need to replace every single word in the sentence, but have a sequence of at least three to four words in the alliteration.
Read the newly converted sentences out loud. If the effect is not what you were looking for, experiment with using a different sound in the alliteration.