What to do about yeast that doesn't work? I am using a new container of yeast from the store; I keep it well-sealed (it's a small jar) and refrigerated. 

I make sure to use warm water in bread recipes - I check the temperature using a digital kitchen thermometer. 

I follow instructions to let the dough rise in a warm, moist environment - I put it in the oven (which is off, but was recently warmed to 100 degrees or so) with a steaming cup of hot water. 

However, my bread still doesn't rise - not in the breadmaker and not when made by hand. 

Should I use more yeast? If so, how much more? (..as in just a pinch more, or as in double or triple the amount?) Should I use more sugar, so the yeast has something to eat? I'm really at a loss here. Should I give it up and use different yeast? If so, what's a trusted brand?
You can proof your yeast to see if its still alive:

Heat approx. ½ cup (100ml) of water to about 115°F (45°C). Add a tablespoon (10g) or so of sugar, stir. Water should still be above 105°F (40°C). Add a teaspoon of yeast, stir. Within 5 minutes or so, the mixture should be thoroughly foamy.

If its not thoroughly foamy, yeast is bad (dead), dispose of it.

(Note: Metric conversions above are rounded, just like the imperial units. Don't use these conversions for baking, but proofing yeast doesn't need anything exact.)