I am new to flyfishing and have a couple of questions. Sinking line and floating line, when would you use one or the other?  I live near a small lake that is for flyfishing only but the only time I've used my fly gear has been on streams. How do you fish still water with fly gear?

Floating lines for  fishing  depths generally 8' or less this could be fish holding at 8 feet over 30 feet of water  you can add split shot to a leader or fish with weighted flys to help get the fly to deeper depths.
and a sinking line for when you want the fly to go deeper . To fish still water  You would strip line in to make the fly look alive . Remember waves and wind will also move a fly around . but for the most part you have to incorporate the movement .

As a new fly fisher, stick with floating line until you get more experience as sinking line is more difficult to pick up off the water and get airborne than floating line. I agree with Rod Tosser on the weighted fly tip for fishing deeper than a floating fly. The weighted fly will pull down your leader and maybe even a little of your fly line depending on what weight you're using. That means you can get down 6 to 9 feet with a weighted fly and still be able to pick up your floating line with ease.

I've been using floating line, I was just curious about the sinking line. I will try the line stripping when I try the place out. Thanks for your help.