Enter the park, hit the gravel, pass two gates then start the long switched back climb. This road is used only by vehicles servicing the Grouse Mountain Ski Resort in summer, so there is rarely traffic. It's not too steep, and when you've had enough, you can always turn around. Don't be surprised to see some snow on the trail in early spring and late fall.
The ski resort has a cafe/restaurant/bar open all year round, and lots of other things to do on a summers day, though you will have to walk your bike once you enter the resort proper.
If the road back down is not adventurous enough, there are numerous downhill single track routes for the way down. 7th Secret (no longer a secret) into Leopard, Kirkford, Crinkum Crankum, Cedar Trail, Upper and Lower Griffen, then a left into McNair makes for a pretty full days riding at an intermediate level (for the North Shore, anyway). Other reasonably mellow rides include Pipeline or Expresso into Lower Crippler or Dempsey Trail, or if you really want a mellower trail, start with Roadside Attraction.
Great maps of Fromme can be found on the Gutsplodder site, and at NSMBA, or ask at your local bike shop for a printed copy of the Fromme map.
More Mt Fromme mountain biking trails can be found here.
Start at the top end of Mountain Hwy on Vancouver's North shore. Park below the orange signs (I think they've got their own personal parking inspector handing out tickets up there), then get on your bike and start climbing.
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