How do you write things that make you want to continue reading? I've got an exciting topic but I don't know how to show this excitement to others through writing. How to make them interested in the topic too? I believe this is the wrong question to ask because you can't force someone to think something is interesting. So you just need to make your idea interesting instead. How does an idea become interesting? That's a much better question!
The specific answer depends heavily on who you are talking to. In general, an interesting idea can be relevant — something the person has been thinking about recently. It can also be a problem solution — if you make the person understand that it will relieve some pain they are having, it will probably be interesting to them. It can be interesting to them if it's close to their belief system and personality — if they believe in something and you are talking about it. Or if they simply feel understood, they feel like someone who is writing this almost knows them.
Now, how do you make your writing relevant, pain-relieving and showing the understanding of a person you are talking to? You really need to understand who you are talking to. It's great if you can imagine a real person with specific traits who you are telling your story to. In some cases you can be this person by yourself, and it's brilliant because nobody knows you better than you. So if you make a story interesting at least to yourself, someone will likely find it interesting too.