In addition to affixing, there are a number of strategies for word formation in English, including functional shift (e.g. turning a noun into a verb, such as "impact" or "text"), clipping and/or blending (e.g. "blog" is probably a blending of the clipped "web" -> "b" and the word "log"; see also "chocoholic" or "morkie"), acronyms (e.g. AIDS or NATO quickly became words themselves), and probably the most widely used strategy of compounding (e.g. "ice cream" or "sex appeal").
A more complicated technique is back-formation, through which part of a word is taken to be a word unto itself. "Pea" (as in green pea soup) is a back-formation from the word "peas." "Peas" used to be a singular collective and non-countable noun (lke "rice" or "corn"), but its -s ending made people start to treat it as a countable plural noun, so they had to invent (through back-formation) the singular form of the word: "pea."
English seems amazing adept at word formation!
One major rule is that English words can be made by agglutination -- by adding affixes to base words. For example, you can start with the word "intention" and add the suffix "al." That makes "intentional" which means "done with intention." To that word, you can add the prefix "un" to create a word meaning "done without intention."
Another major rule is that words can be made by "clipping" -- by shortening longer words to make shorter ones. An example of this is how the word "influenza" has been shortened to "flu."