I just went through this last week. Getting 'The Tenant of Wildfell Hall' for Kindle is straightforward, but the 'how' depends a bit on where you buy it and what device you're using. If you purchase it from Amazon, it'll automatically deliver to your Kindle library linked to that account.
For manual downloading, on a tablet or phone with the Kindle app, you go to your Library, find the book, and tap the cover. There should be a download icon or it might just start. On an actual Kindle e-reader, as long as it's connected to Wi-Fi, purchased books sync automatically. If it doesn't appear, you can go to the 'All' tab in your library and select 'Download' next to the title.
A heads-up on formats: Make sure you're getting the official Kindle edition from Amazon. If you somehow get an EPUB or PDF from elsewhere, you'd need to use the 'Send to Kindle' email feature or a USB cable to transfer it, which is more fuss. The smoothest path is definitely buying or borrowing the Kindle version directly through Amazon. I find the delivery system pretty reliable once your devices are properly registered.