I just struggled through this so I'll provide the way that worked for me. It's definitely not a perfect solution but it was the only way I could find to test my app in the Simulator using the San Francisco font, so at least it worked for that. Even though my app uses "System" as the default font, I couldn't figure out how to get Xcode to use San Francisco instead of Helvetica Neue for "System"--I had to change it to Custom font and specifically choose San Francisco. Also, it appears like you would have to do my fix per project; it doesn't look like it remembers it systemwide.
You said you downloaded the font successfully but I'll provide all the steps starting with that.
I basically followed this website:
http://codewithchris.com/common-mistakes-with-adding-custom-fonts-to-your-ios-app/
First go here (it'll make you enter your developer account) and download the font:
https://developer.apple.com/fonts/
Add the fonts to your project. You don't need to put them in a fonts folder but I did that for organization.
Verify that they appear in the Bundle Resources. I didn't have to do anything here; they just appeared automatically.
Go to your plist file and add them, one line for each font. I did have to do this step. To make it easier, I opened a terminal window and ran the ls command to list the fonts so I could copy/paste each name rather than type them all.
Here's the list in terminal:
Now in the story editor, I could click a control and change its font. This is the part where I don't know how to make Xcode automatically use the San Francisco font when it's set to "System". I had to change it to Custom as shown here:
Once I picked System, I could scroll down and change the font from Helvetica Neue to SF UI Display.
As I said earlier, this trick at least let me test the SF font in the Simulator, but it's not the perfect fix, because ideally all you'd have to do is change it to iOS9 and Xcode would be smart enough to use San Francisco rather than Helvetical Neue, since that's what a real device would do. However, this should at least enable you do see SF in the simulator.