I am using a download manager that supports download from various video sites including YouTube. It's called Free Download Manager and can be used for other downloads as well. There is also a page on the developer's website where you can see the whole procedure. Basically, you add a new link, configure a few options or leave them by default and then continue the download procedure.
To convert the videos to another format, Handbrake can be used as well.
Tip: You can download Free Download Manager from the same page you used to read the instructions.