First keep in mind that with rasterization there technically is no such thing as true resolution independence. With high enough magnification individual texels will start to become visible. The only solution to this is to write a vector graphics system.
That being said there are a few steps to creating a robust raster based resolution independent system: sizing, coordinate systems, and layout.
For sizing and positioning we need to use some set of units that maintain a ratio to the actual application resolution. In this case lets use inches because I'm American and you can scale elements with DPI (dots per inch). For example lets say your application is running at 800x600. Default Windows DPI is 96 so that means the application has a resolution of (800 / 96) x (600 / 96) inches or 8.33x6.25 inches.
Since you need to be able to work with, at the very least, both 4:3 and 16:9 aspect ratios how you handle your screen coordinate system gets a little bit tricky. What I recommend doing is putting (0,0) in the center of the display area (as well as windows and controls). This works well because if you put (0,0) in a corner then as that corner moves around based on resolution and aspect ratio it's going to translate all of your sprites whereas the center of the screen will always be the center of the screen no matter the device. Continuing our example with 800x600 this would result in a coordinate system that is (left to right) -4.165in to 4.165in and (top to bottom) 3.125in to -3.125in.
So at the moment you have DPI independent UI system with items that will always be at the same spot relative to the center of the screen - not quite resolution independent. Fortunately what DPI independence allows you to do is scale the UI by scaling DPI based on some heuristic. For example we can scale DPI using vertical resolution as our heuristic. If 800x600 is 96 DPI then we'll use 123 DPI for 1024x768 or 115 DPI for 1280x720.
Lastly you will need to build a layout system that handles both absolute positioning as well as relative positioning. Excellent examples of this are WPF and the web. You can specify that controls/boxes fill some % of the parent element while docking it to an edge along with many other useful automatic layout options. All of this together will result in a UI system capable of looking nearly identical across many different resolutions and aspect ratios.
To summarize I highly recommend you study WPF as it does nearly all of this except it maintains an origin at the top-left corner coordinate system and doesn't automatically scale DPI based on vertical resolution.