Transfer Songs from Windows Computer to Iphone

Hi All,

I have a question regarding transferring songs from my laptop to my Iphone that I thought would be an easy process. When I connect my iphone to my laptop, I can see the phone as a device within Itunes on my computer. Separately, I can also see all the songs on my laptop in this same itunes. I thought that I could just select and drag some songs and move them over to my iphone (under songs). I can grab the songs and move them to the phone, however, they don't copy over. Also, interestingly, when I open the songs directory of my iphone, I only see the last 3 songs that I purchased. I have hundreds of songs (purchased and from old CDs) on my iphone and can see them when it's not connected to this computer. Can anyone help? I feel like banging my head against the wall!