When you plug in your USB, it will be automatically mounted with some name in the /media folder.
Open a Terminal (Ctrl+Alt+T). Type the following command:
mount
You will see a result something like this:
/dev/sda7 on / type ext4 (rw,errors=remount-ro)
proc on /proc type proc (rw,noexec,nosuid,nodev)
sysfs on /sys type sysfs (rw,noexec,nosuid,nodev)
none on /sys/kernel/debug type debugfs (rw)
devpts on /dev/pts type devpts (rw,noexec,nosuid,gid=5,mode=0620)
tmpfs on /run type tmpfs (rw,noexec,nosuid,size=10%,mode=0755)
none on /run/lock type tmpfs (rw,noexec,nosuid,nodev,size=5242880)
none on /run/shm type tmpfs (rw,nosuid,nodev)
/dev/sda5 on /home type ext4 (rw)
/dev/sdb1 on /media/84CD-D8C7 type vfat (rw,nosuid,nodev,uid=1000,gid=1000,shortname=mixed,dmask=0077,utf8=1,showexec,uhelper=udisks)
Look at the last line in my example: /dev/sdb1 on /media/84CD-D8C7 type vfat plus some other output. Your clue is that its folder begins with /media; in this case, /media/84CD-D8C7.
You can now tell the system to remount it read-only with the following command:
sudo mount --options=remount,ro /media/84CD-D8C7
Of course, you would replace 84CD-D8C7 with the actual name that you have. To check that it worked, you can reissue the mount command. See how mine has changed — look for the ro after the parenthesis (ro stands for "read-only", rw stands for "read-write").
/dev/sdb1 on /media/84CD-D8C7 type vfat (ro,nosuid,nodev,uid=1000,gid=1000,shortname=mixed,dmask=0077,utf8=1,showexec,uhelper=udisks)
Explanation (if you are interested):
sudo means to authorise this command (i.e. run it as "root"), because the "mount" command is not available to all users. This will ask for your password.
mount tells the system to "mount" the device, i.e. attach it to your computer and give it a folder name. In this case, it has already been done; we are using the command to change the way the device was mounted.
--options tells the mount command that we are going to specify some options.
remount means just that: mount the device again, with exactly the same settings unless you tell it otherwise.
ro says to remount as read-only. This is the only change that we are making to the mount.
/media/84CD-D8C7 specifies where it is already mounted.