If you go to the Godot website homepage you will find the big download button in the middle of the page. Simply clicking download latest will bring you to the download page.
It should automatically detect your operating system allow you to press the blue button that says "Godot Engine". You can ignore the .net version as we don't need it.
After it has downloaded you will find it in your downloads folder. After unzipping the zip file (if you don't know how to do this you can right click on it and press unzip) you can exacute the unzipped file and it will simply run. No length instalation process.
By it's very nature Godot is portable. It is, in fact, only a single file. I recommend finding a nice snug place for it to live. If you wish you can plop it straight into your Desktop without any problems