You must have a 3DS for this; you cannot use a PC alone.
Dumping a cartridge does not dump DLC and updates for that cartridge. Those are stored on the SD card. See Dumping Updates and DLCs for more information.
With the onset of sighax and boot9strap, the supported method of dumping game cartridges is GodMode9.
[C:] GAMECART by navigating using the D-Pad and pressing (A).[TitleID]_[version].trim.3ds, then select NCSD image options..., then select Decrypt file (0:/gm9/out)/gm9/out/ to a folder on your computer.You can now use this game with Citra. You can open it directly from the menu bar (File > Load File) or add a folder containing all your dumps by double-clicking the + icon in the main Citra window or by double clicking on Add New Game Directory.