I made these cool test leads at TechShop Pittsburgh, which is just completely awesome. They have several locations, and you should seriously consider paying them a visit and taking a tour if you want access to more powerful tools or want to take classes and learn new useful skills. Check out all the cool stuff they do and the amazing equipment they have at www.techshop.ws
Alligator clips (2)
Short pieces of wire, about 6 inches long (2)
BNC cable (or coaxial cable with BNC adapter, etc.)
Electrical tape or shrink wrap tubing
Soldering equipment and supplies
Wire cutter and/or knife
Step 1: Preparing the cable
First cut off about an inch and a half of the outer layer of coating using the knife or wire cutters. Be careful to only cut through the outer plastic coating.
Now use the wire cutters to cut off the braided wire and foil, if your cable has it. It doesn't have to be perfect, but try to keep it neat.
Next we cut off a section of the inner plastic coating.
We now have access to both conductors of the cable, so we can move on to preparing our clips.
Step 2: Preparing the clips
Step 3: Putting it together
Let's actually connect it now. To get a good connection, you should line up the end of the wire with the cable of the connector so they are touching and parallel to each other. Make sure you have a good solder joint by checking to see that the solder is covering the entire connecting length, not just a single point or blob.
The outer mesh is easier to solder to, but less pretty. Just make sure it is stuck on there really well, and avoid burning through the inner insulating plastic with the soldering iron.
Step 4: Finishing up
Now just test it out to see if it works!