I have a bandsaw. It typically has a 3/4" x 3 tpi resawing blade in it, which is great for making big boards into little boards in a hurry, but not so much for cutting curves. Changing the blade is a ten minute hassle, and for cutting certain items like curved legs or bracket feet that's what I do. But for quick jobs, working on pieces that are too big to take to the bandsaw, or starting in a hole in the middle of a workpiece, an olde timey bowsaw (aka turning saw) is a great tool.
It's basically a big coping saw, using similar narrow blades, but much longer, typically 12". The frame is fairly easy to make from wood, and you can either make your own metal hardware to hold the blades, or buy a set from Tools for Working Wood, who also sell the blades. Bill Anderson is selling a slightly different style of brass pins on his website, too.
Realistically, you can take three sticks and some mason line, drill a few holes, whittle a couple of notches with a knife, insert some hardware, and have a functional saw. You could even take the hardware from a cheap coping saw or make your own from nuts and bolts and make the whole thing really lowbrow. The saw will be much nicer to use, however, if it's shaped carefully to be lightweight while maintaining strength, and comfortable to hold. Plus it's a lot more fun to use beautiful tools, and that goes double when you made it yourself.
There's an episode of the Woodwright's Shop where Roy Underhill and Bill Anderson examine an antique and go through the steps of reproducing it. See that excellent video here. Popular Woodworking did a closely related article with a plan (by Bill Anderson ) in the Nov 2011 issue, and another bowsaw article in Oct 2010. Both of those PWW links have some nice accessory videos and stuff. There's a plan from the 1920's on the "Galootish Gleanings" section of The Cornish Workshop. Tools for Working Wood also has a plan you can print and a page of tips, and Shannon Rogers does a video of his TWW build on his Renaissance Woodworker blog here. Finally, here's another blog entry by Steve Branam.
So there you go. If you visit all those resources, there isn't much I can add, because I don't have any first hand knowledge. I got the Gramercy pins from TWW last week, I'll find some appropriate wood next week, and build my own here soon.
Update: I sliced up some scraps of beech molding on the bandsaw, and made a bowsaw from the straightest-grain sections. I followed TWW's general form and some dimensions, but drew the parts freehand and didn't try to copy their plan slavishly. I reduced the frame components to 9/16" thick before shaping, aiming for a lightweight version. We'll see how it holds up under tension... I also turned a longer handle to fit my hand, with a groove for my thumb near the front. I used 3/32" braided polyester cord for the tensioning mechanism, which doesn't stretch like nylon. I don't know if that matters. I have found that the pins turn a little too easily in their holes, and the saw tends to twist as I use it unless I hold the arm of the saw moreso than the handle. I've found that I either need to wrap my right index finger around the frame, or use both hands, with my left hand on top of my right hand, gripping the frame.