To save you some time from reading the manual, there are only two commands you need.
To clone /dev/sda1 without directories A and B:
Here -jn is the number of thread used, n= 2.. etc. -zn is the compression level, n can be 2, 3 etc. see fsarchiver's quickstart guide to find the level that suits you. /path/to/storage.. is the path to the storage device where you want to save the .fsa file which is called "backup.fsa" here. -a and -A if you want to clone drives which are currently mounted and running. If you are cloning drives that are not mounted (say you clone with the live usb booting off your original machine) then you don't need them. -v for verbose, it is good to have outputs on the terminals or I get nervous. --exclude=.. are optional for you to exclude directories. For examples, --exclude=Downloads --exclude=Music etc. In terminal type man fsarchiver for options.
sudo fsarchiver -v -jn -zn -a -A savefs /path/to/storage/backup.fsa /dev/sda1 --exclude=directory_A --exclude=directory_B
To restore clone to sda2 in same or other machines
Edited: if your usb driver for making the live usb is big enough to hold your .fsa file you won't need an additional storage device. Just make an extra partition in your usb drive for that purpose (I would format it to ext4 but it shouldn't matter as long as it supports the partition size,--FAT doesn't e.g)
sudo fsarchiver -v -jn restfs /path/to/storage/backup.fsa id=0,dest=/dev/sda2