Look up the word paradox in a few different dictionaries, either in book form or online. This will help give you a few different definitions of the word.
Write down the definitions you find for the word paradox that make the most sense to you. Since a paradox can be a complex concept, you might find some definitions that are clearer than others.
Examine what you want to describe in your sentence. What you are describing may or may not be a paradox, and, of course, you should only use the word paradox in your sentence if it is. Use the definitions you found to help you determine this. Generally if what you are describing seems to suggest a contradiction, puzzle or anomaly, it may very well be a paradox. Also, it could be a concept that seems impossible yet is not.
Add the word paradox to your sentence that is describing the concept you're referring to. You can use paradox in a few different ways. For example, you might say, "The paradox of the situation is..." or "The apparent paradox..." to start your sentence. You could also say things like "There are various ways to resolve this paradox" or "There are similar paradoxes found in science and nature."