One way is to check on popular fanfiction websites. Look for ones with high ratings and a lot of reviews. For example, Archive of Our Own (AO3) has a large collection of AOT fanfictions. You can search for the most popular ones there.
It can be a bit tricky to find it for free legally. Sometimes, libraries might have digital copies available for borrowing. But often, free versions are against copyright laws and not recommended.
First, get to know the Attack on Titan world really well. Read the manga, watch the anime. Then, create your original character. Decide on their appearance, personality, and backstory. After that, think of a plot that can incorporate your OC into the AOT universe.
Another difference lies in the overall mood. Canon AOT has a rather dark, gritty, and often hopeless mood due to the constant threat of Titans. However, a friendly Titan fanfic would likely have a more positive, hopeful mood. It might explore themes of redemption for the Titans, or how their existence could be beneficial to the world of AOT. This is a complete departure from the doom - and - gloom feeling that often pervades the official AOT story.