A tall tale is a lot like a fairy tale, but there are some differences that make it special.
A tall tale is usually based on a true story, but someone took the things that were true about that story, and changed them a little. These changes are usually exaggerations. An exaggeration is kind of like a lie, but it's meant more as a joke. For example, you might say "That tree was a thousand feet tall!" - trees aren't really a thousand feet tall, but this makes us understand that this was a VERY big tree. It is often said that tall tales are "larger than life" - so think about this when you write your story.
The best thing you can do to write a story is to write about something that you know a lot about. If you have a pet, you could write about what you and your pet do together, but remember to make it "larger than life". If you took a dog for a walk, don't say you walked down the street, say you walked to Alaska. If you made dinner, say that you baked a hundred pies and fed everyone in your neighborhood.
You can also read some tall tales and look carefully at how they're written. Paul Bunyan is probably the most famous example.