Let me show you how to do it - it's pretty easy.
Run iTunes and choose File --> New Playlist. Now rename it to something else: for example, "iPhone Sync":Now you can just drag-n-drop music from your iTunes library (from your PC, actually) into this new playlist. When you're ready, you'll see a bunch of MP3 files happily ensconced in the playlist (remember, it's all just "pointers": the actual music files are still safely in the main music library, so if you delete something from a playlist , you haven't deleted the original music file itself):
Notice here on the very bottom of the iTunes window it shows you how many songs are in the playlist, together with total size and playing time.
At this point, you need to plug in your iPhone if you haven't already done so. It'll pop up the usual summary screen:
Nice. Now click on the "Music" tab and you'll see that you can select "sync playlist". Do that, then select the new iPhone sync playlist you've created, as shown here:
Set things up just as I have shown and that's all there is to it. Now click "Sync" in iTunes and it'll synchronize your playlist with the iPhone music library and next time you click on that button on the iPhone, your selections from you music library will be present.
Oh, and one really nice feature of creating this playlist is that you can manage it, adding and deleting songs to your heart's desire, even without your iPhone present. Whatever changes you make are instantly applied to your iPhone music library the very next time you synchronize the device.
Now that you know how to transfer music from PC to iPhone, learning how to Download Music from the Internet shouldn't be a problem for you :)