From within Linux, open a terminal window. As root user (sudo in Ubuntu), use:
dd if=/dev/olddrive of=/dev/newdrive bs=32M
where /dev/olddrive points to the source disk (like for example /dev/sdd) and /dev/newdrive points to the new blank disk (like for example /dev/sde). Your target drive will be overwritten and if it contained data it will be lost forever!
WARNING: Before you even try using the above command, check the following:
1. You can't use dd on a live Linux system. That is, if you want to copy your USB drive, don't boot from it !!! So the best is to boot into a live Linux USB stick. If that is not an option, you need to mount your Linux file system on the USB drive to "read only".
2. Make absolutely certain that you specify the right source and destination drives !!! The command df should list the mounted file systems. Check to make sure you got it right, else dd will happily overwrite an existing disk with data on it. Don't mix up the if= and of= command option - "if" stands for input file and "of" for output file, though in this case you clone an entire disk!
3. The target drive MUST be equal or larger in size than the source drive (USB disk), else dd will fail.
There are zillions of options for dd, you can also create an img image file of the entire disk, or use dd in combination with gzip and an image file to get a compressed image file on your target drive.
If used with great caution (!!!), dd is your best friend for cloning. It copies the entire disk with boot sector and MBR and partition table etc. to the target drive.
If the target disk is larger than your source disk, you will have some unused space on it. That's no problem as you can easily format that extra space (or resize your partitions) to make use of it.
By the way, dragging and pasting won't give you a bootable disk! You can do that and then install your MBR and/or bootloader manually, but that's a pain in the neck. Again, you can't use drag and drop when you boot from your USB drive (see point 1 above).
A final note on dd: it won't give you any progress indication and it WILL take a long time, depending on the size of your USB drive. It will copy the entire drive, so be prepared for some hours of waiting until it completes.
Good luck!