This is a very simple project that should take about 20 minutes to build. Find a small spring with a 30 - 50mm end piece. See the pictures, mine came from a scrap CD-ROM drive but you'll find suitable candidates in all sorts of electromechanical consumer goods. Then find a screw about 15 - 20mm long that fits through the coiled part of the spring.
The body of the project is a piece of softwood, roughly 50mmx10mmx200mm. Cut a 50mm piece off the end of it and in the 50mm piece machine out a T-shaped slot to hold the coiled part of the spring with the screw through the middle of it. See pictures for a close-up. I used a Dremel for this, you could just as easily use a small chisel or even a knife.
With the spring and screw in the slot, screw the 50mm piece onto the remainder of the wood such that it traps spring and screw. I drilled a couple of guide holes to take the screws in mine, you may choose not to.
You should now have a completed spring clamp. To use it, place the board under the spring with the end of the spring coming down onto the place your component will go. Carefully unpack the component - in the pictures it's a 1206 chip resistor - onto the board, lift up the spring and edge the component into position before letting the spring down to hold it in place. You can then apply some flux, solder each end, and use a bit of desolder braid to remove excess without having to worry about holding the component down.