Kevin,
Found a link to a van service that may be of help. It's called "Airways Transit", and I priced a YYZ to Hamilton fare on their website. It shows $61 CAD, which is kind of high for such a short trip (about 30 miles). But if it helps, here's their website:
www.airwaystransit.com
Your might consider renting a car at the airport (all the major car rental agencies are at YYZ), which would give you more flexibility if you need to get around the area. It's an easy drive on good highways form YYZ to Hamilton, and the rental fees might work out less than the $122 roundtrip for the van service.
Other than that, bus into Toronto, then use the "GO Transit" bus or train from Union Station in downtown Toronto to get to Hamilton. Note that weekend service is reduced though, so you'd be best to check their schedules if you're pressed for time. This would be your cheapest option, but much longer timewise.
There are also airline limousine services at the airport, but these will be quite expensive for a Hamilton trip.
Hope this helps. Good luck on your trip.
bj-21.