First, load up Apple's Retail site, apple.com/retail. When you get there, feed it your zip code to get the list of stores in your area. Once the list shows, you can choose one:
Here's the list I get in my area. What a pretty store!
When you get the details page for the store, you can click on Genius Bar to get your options. If you're already signed in you will see your registered hardware, and you can choose from that list. If you don't see your own items, you can choose from a list of Apple hardware on the page, then move on to the next step:
What are you having trouble with? Let's get started!
Next up will be “What's happening with…” which will give you some options to choose from to narrow down your issue. Whatever you pick, you'll get a common list of topics that might assist you. If they look helpful, go that route, but otherwise just pick something and you'll get the next steps.
If your issue isn't listed you get to fill it in.
Depending what you choose, you might see Genius Bar at the top as one of your “main” options, or it might be listed at the bottom under the other options:
Listed at the bottom, I guess you can make a Genius Bar appointment if you really want to…
Once you have chosen the Genius Bar, you can work through the time and date of your appointment and Apple ID signup. Then you'll be all set to take your hardware in, no app required.