You'll see dried ginger in powder form in the spice aisle in any grocery store, but absolutely use fresh. The flavor is deeper and sweeter in my cooking experience, though I've not brewed a beer with it yet. You'll definitely need more fresh than dried. For cooking, I've seen anywhere from 1:4 to 1:8 substitutions. I agree with Billl's methodology, though, so you don't overdo it.
Having tried both with the same recipe, I couldn't agree more. Definitely use fresh, and you'll definitely need more than 1oz.
Powered/dry ginger is gross by comparison and I've had trouble getting it to dissolve.
If you do use fresh ginger, you'll need to slice it up (I peel first), add it to a pot of water, bring to a boil, then simmer for about half an hour.
I like a strong ginger burn (when I say strong, I mean it! I make 14% abv ginger wine and you can taste the ginger more than the alcohol) and use about 9-11 oz per gallon of end product.
If you like ginger but you're not obsessed with it like I am, you'll probably want like 3-4oz fresh per gallon if you want the ginger to be noticeable but not burn.
I've heard it's good to freeze it and thaw it before you boil it to get more flavor. I haven't tried it but you might give it a shot.
Honestly, though, I wouldn't worry about overdoing the ginger. Worst case scenario, add more water to dilute it and dump a little excess out. Or save it for something else.