There are manual ways to download YouTube files, but if you want to do things the easy way download an application called GetTube and let it do the heavy lifting. You can use this link for the direct download.
Once you have downloaded the application you just need to set up the download location in the preferences window.
Then open up the GetTube application window and find the YouTube file you want to download. GetTube has an in-app browser so no need to switch to Safari.
You will notice a very small download button in the lower right corner. Just click the button and a dialog box will pop up asking you the format you want to save the file as.
Do you want the video or just the audio? Pick one and hit download. After a while your download will be done!
Just go to the download location you specified to find your file and you're done. Couldn't be easier.