Whenever you are asked to find smaller words contained within a larger one, you are looking for incomplete or subliminal anagrams. Although there are many online tools that can unscramble letters, you can find many words on your own using some simple strategies.
Pull out any words that are already there
Look for smaller words that are present in the larger word before any rearranging. If the larger word has multiple prefixes or suffixes, remove or cover them so you can see the root word. Write these words as you find them. For example, if you are looking at the word "deodorant," start with "odor" and "ant."
Rearrange the letters
Scramble or reorganize the letters so you can recognize new patterns. You could take, for example, every third letter to write them in a new order. For the word "deodorant," taking every third letter would produce "ortdnoead." You could also try putting the letters into a random grid, as they might appear in the game Boggle.
Use found words to find others that are similar
Once you have found a word, look for prefixes or suffixes present in the original word that can be added. Try exchanging or adding one letter at a time to the beginning or the end. Also look for similar sounding or rhyming words. For example, when working with "deodorant," you could use "ran" as a base to help you find "rant" and "ranted."