How to get songs from a CD to an iPhone?

I put the cd on my computer and this has happened for around 4 other cds. I had a cd downloaded onto my phone and did it by checking the artist name but even now it comes up faded out and when i try and click on it, it doesn't play the song. Its frustrating and strange why can't I get music from a cd thats imported to itunes on my phone.
Heres a picture of what it looks like on my phone

Assuming you are using windows here are the instructions http://www.justtext.com/messageboards/20130322165821.html

Try opening iTunes with your iPhone plugged into your computer.

With 1 of your CDs in your computer, open up the computer folder with all of the songs listed.

Select all of the songs (Shift + Drag your mouse over all of the songs) and DRAG the songs to your iTunes. DON'T let go of the songs until you move your mouse to the left side of iTunes over the name of your iPhone. (A "plus sign" should appear.) After that it should say that the music is importing into your iPhone.