That depends on your browser mainly. Most of them have a default 'downloads' folder.
If you open the 'downloads' tab in your browser (in Firefox it's 'Tools > Downloads' and in Chrome it's 'Options > Downloads') you'll find a 'downloads folder' or 'open containing folder' button.
Click this and it'll open your computer's finder window or windows explorer program.
You will see your APK here. You can copy it to a more easily locatable spot on your computer if you wish.