Providing you have fitted an internal HDD, or external storage device, it's quite simple.
You set up the download option, in the KODI addon, via the options.
Take Scrubs v2, as an example, as this is one of the more difficult to setup.
Enter KODI, go to ADDONS and select Scrubs v2.
Scroll to Tools and press OK.
Scroll to General Settings and press OK.
Scroll all the way down, to Special Settings, and press the right arrow, on your centre remote, to access your options.
Scroll down to Download section, and enable downloads. Once done scroll down to Movies, press OK, and navigate to your recording location, with an internal hard drive it should be Media folder, then HDD, then Movie, once done hit the right arrow, twice, until you're on OK and select it, using your remote OK button. Now scroll down to TV and do the same.
With other Addons it's usually easier.
Like The Crew, enter this Addon, scroll to Tools, Settings General, scroll down to Downloads, Enable Downloads and set up the Movie, and TV, options as above.
There are illustrated guides, like this one, which are quite old now, but still useful:
Code:
https://kinkeadtech.com/download-in-kodi/
Once you've set up your downloads, search for a stream, as usual, but instead of playing hit press the menu button, on your remote, and select the Download option. Not all streams are available, for download, or playing, for that matter, but usually you will find one.