Just in case you didn't know - you'll actually have to get to the Burlington GO station (not Hamilton) in order to take trains on weekends, since it's only weekday train service from Hamilton (and even then it's quite limited).
But if you can get down to the Hamilton GO station via the HSR, then you can take a GO bus from there to Burlington to meet your train. If it were a weekday, you could take a GO bus directly from the Mac GO station to Burlington, but they don't offer this service on weekends. You'll need to wait for someone else to chime in as to the best HSR route to take, since I never needed to do that, but here's the Saturday GO schedule:
http://www.gotransit.com/publicroot/...p age=1&new=Y
The yellow boxes are buses, the green boxes are trains.
Note that this is the Lakeshore West line, but after Union Station you'll be switching over to the Lakeshore East line - I'm pretty sure most trains just continue on, though.