Well, you can't really go to youtube and download just the song. You can download a video from youtube my copying the URL and going to savevid.com ([link removed] ) and clicking download. I have a Macbook pro, so my computer will probably download it defferently than a Windows or anything else, but download it and then try sending it to your phone. You will get the video in a picture mail or something and make sure you let the video play on your phone first before you save it or download it, just so you know it's the right video. If you want to download just the song, you can download Frostwire or Limewire to your computer and get the song there.
I'm pretty sure you have to put them on using a USB cable. You can download the song on your pc. There are YouTube converters that can convert the video to mp3 and let you download it or you can download the full video. Once you've downloaded it, plug your phone in your pc with the cable and your phone user manual should tell you how you put music or videos on to the phone. :)
You can use a program called JDownloader. It will allow you by simply copying the link of the Youtube video into the program to download the audio from the video hassle free.
Then connect your phone, and depending on your phone put the song in the music folder.