I recently got into Xamarin development. I have a lot of experience in Xcode making iOS apps and the iOS side was very straight forward. Now I'm trying to implement Android. I downloaded a Hello World example to get my bearings. When I run it I have no problems getting the simulator to show up (MonoForAndroid_API_10 and MonoForAndroid_API_12) but the actual application doesn't run, and does not show up anywhere on the simulator. Essentially whenever I use run or run with in Xamarin on Android, it pulls up a fully functioning, albeit empty simulator.
How do I get my application to run on the emulator?
Like the other commenters, this is most likely just a symptom of slow emulator on your machine. I'm running Xamarin-Android development on my 2010-era OSX machine in mavericks with 8GB RAM, and it is slow-slow-slow, but usable. Try to find the Intel x86 speeds improvements (look for HAXM) and you will find that the emulator will be much much faster.
And yeah, get a real handset and plug it in to your computer: always much faster than emulation.
later edit Get Genymotion for Mac OSX or for PC/Windows or PC/Linux. It's way way way faster than the other emulators. I have since found that this is as fast, or faster, than running the App on my connected Android phone. It's certainly simpler in not having to have the device plugged into one of my USB ports, and allows me to code and test on the train. http://www.genymotion.com/