I'm helping a friend out as the come to the end of their AWS free tier time. They've been with AWS about a year, and their billing meter has started to run, so they wanted to check in on things. So, I did.
First thing to know is the free tier instance is always above the smallest, which I think includes mini and nano, but the eligible size is small. I think this is partly because this is a more reasonable size for project work, but also because most people I think won't adjust things, and you end up paying more. Also, they throw in 30GB/mo of block storage, but most boxes only need 8GB for the OS, and usually the default is SSD storage.
So, the easiest way to save money is two small changes -- downsize your instance type, and flip over your storage media. By using standard (spinning drives), you pay half what you do with SSD storage. By moving to a lighter instance type, you can save 40-50% or more. Both of these are just a few clicks to get working.
A slightly harder but bigger potential discount is spot instances. The risk of spot is price variability, and the chance if you set a max price is that your instance can be stopped. For this, discounts of 60-70% are available. With spot, its more likely you'll need an AMI, and also you need to understand how to set things up -- there is a bit of a learning curve with how to get spot instances going.