How can I see more detailed information about my skills?

In looking at the skills on my Barbarian, I can't really tell what effect they might have on damage.

For instance, I understand that Bash generates 6 rage when I attack, but does the "brutal strike" it describes translate into it actually doing more damage than a default melee attack?

Similarly, the Cleave skills indicates that it "swings your weapon in an arc to hit multiple enemies", but doesn't say how big the arc is, how many enemies can be hit, or what effect it might have on damage. It isn't unusual in games like this for a skill like cleave to do less damage than a standard attack to each individual enemy, but from the skill description, I have no way to know if that's the case here. Most Diablo clones, and indeed even Diablo 2, give descriptive information about these sorts of things, making me think it might be buried somewhere and I just haven't found it.

Is there anything in the game that gives a more detailed description of the combat effects of skills?

Under the Skills menu, mouseover the skill's image and hold Ctrl. This will expand the tooltip to show detailed information. This also works in the skill selection menu and the hotbar.

There is also an option to show detailed information by default. Go to Options > Gameplay and check the Show Advanced Tooltips option.