Installing and Running X Code and the IOS

Okay this is not exactly a programming questions per se, but I'm new with my Mac and I don't understand how to run/start my Xcode program. I read that since it's different from Windows, many newbies don't really understand how to install an application.. They end up using it under the wrong path etc, when it should be in the Applications folder.....I think.

So I installed my download for XCode and IOS, it all seemed to go fine, but I don't know how to run the program, there is no desktop icon, and I looked all through Finder (the best I know how to) there appear to be 3 panes in finder, devices, places, and search for. I see the xcode in the devices, but that links to the little white hard drive thing on the desktop and just launches the install again (which I already installed) Of course it doesn't look like there is anything useful in the search for area, and in the places pane, I looked under my name folder, desktop (empty, new Mac just bought two days ago) and documents. I don't see an executable file or anything for x code. I only see the xcode install folders, there are two, one brings up the download box as if it's going to download the file again, and the other launches installation.

Then I looked in the Applications folder on the dock, I don't see it in there anywhere, and I looked in other folders within also.

Then listening to a suggestion from another thread, I used the search glass at the top of my desktop I see the xcode there, and I can launch the program, so all is good, right?

Maybe, but I still don't know where the program actually is. It's not in my applications folder I'm pretty sure. So where is it? Do I always have to go to the search glass to launch a program? Probably not.

Secondly, if I start using my xcode and it's not in the right folder or path won't that potentially cause problems down the road? It should be in applications right?

Thanks
Scott