There is a script to get it working on Ubuntu Forums.
sudo add-apt-repository ppa:conky-companions/ppa
sudo apt-get update && sudo apt-get install conkygooglecalendar
Add to your .conkyrc:
${execpi 1800 conkyGoogleCalendar
--username=yourname@gmail.com --password=yourpassword --daysahead=30 --dateformat="%a %d %b, %y" --requestCalendarNames="MyCalendar1;MyCalendar2"
--template=~/scripts/conkyGoogleCalendar.template}
Replace MyCalendar1 and MyCalendar2 with the name of your Calendar/Tasks.
Create a template, in this case there is a template in ~/scripts/ named conkyGoogleCalendar.template.
Example of this template:
${color4}${font Ubuntusize=10}Event: ${font Ubuntu:bold:size=10} ${color3}[title]
${color2}${font Ubuntu:size=8}Start:$font ${color1}[starttime]
${color2}${font Ubuntu:size=8}End:$font ${color1}[endtime]
${color2}${font Ubuntu:size=8}Description:$font ${color1}[description]
${color2}${font Ubuntu:size=8}Place:$font ${color1}[location]
You can take a look at the "Conky companions" here.
There is a README file within the package with clear instructions.