Bike Pump: Am I doing it wrong?

I've got a bike. I've got a compatible pump (two actually!). So why can't I seem to get the tires full enough to ride on? NB: I'm starting from completely flat tires (it's been a long time since I've ridden the bike). Is it not possible to hand pump bike tires all the way from flat?
posted by ocherdraco on Jan 24, 2013 - 45 answers