First of all check that /dev/ttyACM0 actually exists. Do something like 'ls -la /dev/ttyACM0' and look at the output. After that things start to differentiate depending on a distributive.
You may need to add your used to some group (often called 'dialout').
I typically just create a UDEV rule to let anyone use the port. Again, depends on the distro. In Debian based it will be something like this. Create a file /etc/udev/rules.d/90-ftdi-cable.rules (name it whatever you want, of course). The contents of the file should be something like this:
ATTRS{idVendor}=="0403", ATTRS{idProduct}=="6001", MODE="0666"
Substitute correct VID and PID for your device. Unplug and re-plug the device. This will give everyone RW access.