Actually, likely nothing will happen when you plug in your DX, but it should have the charging lightning across the battery icon at the top of the home page.
To access the DX's SD card, you need to open your computer's own folder and click on the drive letter assigned to your DX. Then you have access to your SD card and can drag/drop back and forth between your computer and DX for such as photos, music files, ring tones, wallpapers, etc. Just make sure they are put into the right folders on the SD card.
You can also edit folders on the SD card, such as sorting/deleting photos, moving those you want to save into your computer's files (to clear out the DX folder), etc. The SD card functions like a flash drive.