To download and install Resolve, you can find a step by step walkthrough here.. If you're on a Mac, it's recently been added to the App Store as well! There's no real difference installing it from the App Store, or from Black Magic's website, though the App Store may be a bit faster.
The file browser for Resolve is built right into the landing page for every project, known as the Media tab, you can always return to this through the tab on the far left on the bottom, marked Media if you hover over it.
To start off, navigate through your file system to wherever you've stored your footage.
Click and drag that footage down into the Media Browser area(the space with the alternating grey lines). It will likely prompt you to change your project settings. Feel free to
Accept, you'll always have the option to change this later.
From here, you'll need to navigate over to the
Edit tab, the third one in from the left. This can also be done in the
Cut tab, but everything you can do in
Cut can be done in
Edit, but not vice versa. For this reason, I recommend doing the majority of your work in Edit, this will also make it significantly easier if you want to transfer your skills over to Premiere or FCPX, as the
Edit workspace closely resembles them.
Once you're in the
Edit Tab, you can double click any of your clips in order to see them in your Preview screen. Once you've found what you're looking for, you can start dragging your clips down to your timeline!