First, your work machine would need to have a static IP address and permanent Internet connection, and its firewall should be configured to allow access to port 3306 (or whatever port your MySQL installation uses).
Then, on your home machine, just point any client programs to use the IP address of your work machine and its MySQL port number. You could also install something like MySQL Control Centre if you like.
If your work MySQL installation is not already exposed to the world, then you would want to make sure that its passwords and user privileges are fairly tightly controlled before opening it up.
I hope that works for you.