Retry the URL from the address bar again by clicking the reload/refresh button or pressing F5.
Even though the 503 Service Unavailable error means that there's an error on another computer, the issue is probably only temporary. Sometimes just trying the page again will work.
Restart your router and then your computer or device, especially if you're seeing the "Service Unavailable - DNS Failure" error.
While the 503 error is still most likely the fault of the web site you're visiting, it's possible that there's an issue with your computer's or router's DNS server configurations and a simple restart of both might fix the problem.
Important: If the 503 Service Unavailable error message appears while paying for an online purchase, be aware that multiple attempts to checkout may end up creating multiple orders - and multiple charges! Most payment systems, and some credit card companies, have protections from this kind of thing but it's still something to be aware of.
Tip: If resetting your equipment didn't correct the 503 DNS Failure error, there may be temporary issues with the DNS servers themselves. In this case, pick new DNS servers.