除了……以外 (chúle... yǐwài) sets one thing apart from the rest. Whether it means "except" or "besides" depends on the word that comes next: 都 for "except", 还 or 也 for "besides" or "as well as".
除了 + A + 以外，(subject) + 都 + verb.
When the second part has 都 (all), A is the one exception: everyone or everything else is included, but not A. 以外 is optional, so 除了这个字 and 除了这个字以外 mean the same.
除了 + A + 以外，(subject) + 还 / 也 + verb.
When the second part has 还 or 也, A is included and something is added to it. 还 usually adds something else that the same person does. 也 is common when a different person does the same thing.
The subject can come before 除了 or after the 除了 part: 我除了游泳以外 and 除了游泳以外，我 are both fine. 都, 还 and 也 always go after the subject and before the verb, so 除了他，都我们去了 is wrong.
The most common mistake is to leave out 都 or 还, or to use the wrong one. They change the meaning completely: 除了他，我们都去了 means he didn't go, while 除了他，我们也去了 means he went and so did we.
With 都不 or 都没有, the sentence means "nobody but" or "nothing but". To ask "what else?" or "who else?", use 还 with a question word.
Practise this grammar point on paper: 17 exercises using only HSK 3 words, with an answer key on a separate page. Free to print and copy for your class.
Every example on this page uses only words up to HSK 3. Paste your own sentences into the level checker to see which words, if any, are above your level.