Please forgive me if I've written about this before - I've had a quick search & couldn't find it so thought I'd add it :)
I use fold-over stories regularly with my Year 11 class to get them focusing on conjunctions, story-writing, character descriptions and general extending writing techniques.
Each student will need a pen or pencil and a sheet of lined paper. I like to get the students sitting in a circle to make passing things on easier, but they do need to be at a desk or have something to lean on while writing.
Firstly, each student writes the start of a story on their page, then they fold it over so that only the last line can be seen. (This could be as few as one word, or 3 or 4 words, or a whole line if you prefer.) I ask that the students end mid-sentence.
Once they have folded the page over to hide most of what they have written, they pass it on to the person to their left, who now has to write the next part of the story without knowing what has come before. They write a sentence to continue the story (or a few sentences - up to you to decide how much you ask them to write!), then fold it so only the last line is visible and pass it to their left.
This keeps going until the end of the page (or when you decide to finish the activity). The student now writes the ending of the story folds it over and passes it on one more time.
When everyone has finished, the students unfold the story and read it quietly - you can help with understanding as necessary. Ask for some volunteers to read or translate (or read and translate) the story, or perhaps ask for some great examples for you to read & translate to the class. Make sure that you leave time for this, as the stories are nonsensical and often very funny - and it's great to have students really trying to comprehend and collaborating to understand like they do with this activity.
I get the students to rewrite the story correcting any spelling or grammatical errors they notice in the story that they have ended up with for homework as an extra activity (both to practice grammar & spelling, and to encourage them to focus on spelling and grammar as they write), but then I'm mean like that ;) They don't write their name on it at any point, so the mistakes are somewhat anonymous.
This can be done in small to medium groups sitting in a circle, or as a whole class :)