My recollection is that you can download a self extracting .bin file and run that to install Qt. Unfortunately they make it complicated sometimes because the package is so capable that you may find a ton of download links on their download page. Here's a link I found that does online install for three different system types, OS-X, Windows, and Linux:
http://www.qt.io/download-open-source/
For what it's worth, I don't agree with using the creator program. When I got involved with Qt, still use it actually, but also use Visual Studio and program in C++, C# for Windows, but do Qt and other for Linux; all examples were source code. Further, since you have to do something substantive once you activate widgets on the screen, it's best to understand what's under the code. The next point is that when you start doing a next level of programming, like opening files, or reading from a serial port, you need to make threads or use other processes and communicate between them to avoid making the main GUI non-responsive or to avoid blocking a receiver because the program was updating the screen. All that stuff is not offered by the creator, all the creator does IMHO is allow you to place widgets up, align them, and so forth. All of which you can do once you understand how to create and locate a widget. So start with the creator to see what it's doing, but I recommend you move towards understanding the code, or at least understanding how far the creator can take you while understanding where you'll need to begin with code actions. A lot of the special behaviors, styles such as coloring and special shapes, or extensions of behaviors which are non-standard, once again I've always searched and found code examples rather than descriptions of mouse or screen actions which would accomplish what the questioner wanted.
There's extensive documentation provide for deploying a Qt application. It all depends if you build it for shared libraries (their default) or make static applications. I started with static applications and they work fine. If you go to cross compile and install on a totally different system, this also requires a good amount of set up. The only recommendations I can make their are to start fundamentally with a basic program and validate that you got it working a'la compile on one machine, deploy to the target, and verify that it's working. Once you get a basic example working, you should be fine moving into more complicated programs.
As far as libraries. To start with, it's probably best to look for pre-compiled libraries for the target. If you build and run all on x86 machines, then the libraries will be on your build machine. If you build to run on a target, either the target libraries are cross compiled on your build machine and can be made to be part of your deployment, if you build as static then libraries are not an issue, or your target when properly set up should also have libraries on it. Getting pre-compiled libraries for a target is useful because it saves you the steps of building those libraries on your target. Worse comes to worse, yes you can build the libraries on your target, which requires you to configure Qt. Once again, there's a lot of documentation for it. Case by case, it would be best to search for exactly whe you intend to do, or write a topic with highly specific questions, while also showing your attempts up to that point.
Best of luck. Sorry, for the extensive comments; it's not so bad if you just install via the web and run on your machine. I do suggest you start there to get familiar with it, then expand as you go.
