Generally, on my Cross Check (2x10, 46-36 with 12-25), I use the small ring from a stop and shift through about 7 or 8 cogs in the rear as I accelerate then, if I still want to go faster, shift to the big ring in the front and down a gear (to a bigger cog) in the back then continue shifting to smaller cogs until I hit the top (which in practice I never do). When slowing down, I reverse this pattern.

On my Kona Jake, which has a 50-39-30 triple, I almost always use the middle chain ring, only switching to the 30T ring for climbing steep hills and only using the 50T ring when I want to go really fast.