The wifi connection is very weak on both public and private neworks. It's extremely slow at work, home and the gym (the three places where I use wifi the most). The wireless networks at work and home are both private and are Apple wireless routers; an Airport Express and an Airport Extreme at work and a Time Capsule at home. In both the work and home networks, there is a 5Ghz option available. But it doesn't seem to make a difference. I have no idea what the network at my gym is. I just know it's public.
There is an iPhone 4 user here at my office and at home. Both people have no problems with wifi speeds. Same goes for our iPad 2. Wifi works just fine. The people in my office who own iPhone 5s have also said to me that they don't even bother using wifi becuase it's just too slow. I have personally used an iPhone 3G and and iPhone 4 on the same networks that I'm haveing problems with in the past and have never experienced the speed issue until I got the iPhone 5. So that's the only reason why I suspect it has something to do with the iPhone itself.
It is slow in an number of applications. From streaming video and music, to downloading apps, sending photos via text messaging, to browsing the web etc. etc.... it's slow slow slow. I will have wifi turned on, and will have trouble listening to Spotify, or watching something on YouTube. As soon as I turn Wifi off and use the LTE data connection, it zips right along.
I gave up on wifi on my iPhone 5 some time ago and just started using the data connection only. But now that AT&T has started throttling customers with unlimited plans who reach a certain usage percentage each month, I'm now revisiting the problem and trying to find a solution.
I have not done any speed testing. I'm not really sure what is the best way to do that. I'm guessing an app?
As for troubleshooting, I've done simple things like power off and on the phone, resetting the network, "Forgetting" the networks on the phone and then reconnecting. Not much else though.
I'll admit, I am somewhat "clueless," as you say, about the more technical aspects of wifi networking and how they are configured. But that doesn't mean I'm not willing to try a few things. I just don't know enough to even know where to start.