These tips will help you write an application with better chances of being approved.
1. Use proper grammar and spelling
This is in the rules for the applications, but not everyone follows this rule. Using proper grammar shows that you have put some thought into the application. It also shows your maturity as well.
2. Make the questions the proper length
When the old member apps were still around, many applications were rejected just because people ignored how long the second question was supposed to be. Do not be one of the people whose app was rejected because you answered a question in say 25 words when it was supposed to be 75.
3. Put some time into it/'See it from a different perspective'
Make it a good application that you are proud of. After writing it out, look at it again from the eyes of the people who will be approving/rejecting it. See if it is an application that you would approve if you were in their place. If it is not, think of some ways you can improve it.
These are it for now. I might add more later, but hopefully this helps you when you make an application on Terra Nova.