Are you trying to copy files to the SIM card storage or is there a MicroSD card in the phone as well? Does your phone require you to load any software (or driver) on the PC? Some do - some don't.
Usually, when hooked up via USB you see the phone as a new removeable drive on the computer and can view it's folders, create new folders, and copy files just like any other drive, or USB flash drive.
It would help to know what OS your computer has and what phone you are using. Some phones just use the built in OS sync app like Windows Mobile Device Center (or Active Sync if your using XP) and some phones have their own sync app.