The best way to read the AOT manga is to get it in a format that suits you, like physical copies or digital. Make sure you have a clear understanding of the characters and the world-building. Read at your own pace, pausing to think about the plot developments and enjoying the art style.
You can start by finding a reliable source to access the manga, like official manga apps or websites. Then, just start from the first chapter and follow the panels and text to understand the story.
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.
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.
Sure, why not? The AOT manga provides a deeper dive into the world and characters. It can enhance your understanding of the story and give you more background and nuances that might not be fully explored in the anime.