Syncing only checked songs in iTunes is as simple as changing a setting and checking some boxes. To do it, begin by syncing your iPhone or iPod to your computer. When the sync has completed, you should see the management screen in the main iTunes windows.
Check the "Sync only checked songs and videos" box
In the center of the management screen, you'll see a box that reads Sync only checked songs and videos. Click in this box so that a checkmark appears to turn on the ability to only sync checked items. Once you've done that, be sure to click Apply at the bottom-right corner to save the setting and re-sync your device.
Return to Your Music Library
Click the Music icon in the tray at the top left of iTunes. This brings you back to your library, where you can choose what songs you don't want to add to your iPhone or iPod.
Next to each song in iTunes is a little checkbox. By default, all songs are checked and thus will be synced to your device. To choose what songs will be synced, you'll need to uncheck them. Go through your music library and uncheck each song you don't want to have synced to your iPhone or iPod.
Unfortunately, there is no way to uncheck items in bulk, so you have to do it one at a time. Obviously, if you have a lot of music you want to uncheck, this can take a long (potentially very long) time. In that case, you may want to investigate other methods of controlling what music you sync.
When you've completed unchecking all the songs you don't want, click Sync again. If any of the unchecked songs are already on your device, they'll be removed. You can always add them back by re-checking the box next to the song and syncing again.
Want another technique? Keep reading to learn how to use playlists to do the same thing.