Download the CH34x Driver Sources
On the Raspberry Pi, go to http://www.wch.cn/download/CH341SER_LINUX_ZIP.html and click that big blue Download button. This is the manufacturer's website, but it's all in Chinese.
Prepare the Kernel Build Environment
sudo apt-get -y install linux-headers-rpi
sudo apt-get install rpi-update
sudo rpi-update
_ reboot here, you're on the latest kernel_
sudo wget https://raw.githubusercontent.com/notro/rpi-source/master/rpi-source -O /usr/bin/rpi-source && sudo chmod +x /usr/bin/rpi-source && /usr/bin/rpi-source -q --tag-update
sudo apt-get install bc
sudo apt-get install libncurses5-dev
rpi-source
Build the Driver Module
unzip the driver sources archive
cd into the new directory
make