Hi,
I'm not sure what OS you use (Mac or Win) but the storage should show as a External drive when connected via USB to your computer where you could copy or move the images to a folder on the hard drive, otherwise you can use Nikon Transfer which is a part of Nikon View NX2 to transfer the NEF files to your hard disk.
WARNING: If you are using Nikon Transfer make sure you use the latest version as I believe there were some issues with previous versions, if you have used the previous version of Nikon Transfer and the files are corrupted follow the instructions in this post: Re: NEF Files w/ D610