... using a "Connector From Hell", or "CFH", as featured and explained in this thread about making power supply cables:
As with all of my tips and tricks, read through the whole description and make sure you really want to do it (at your own risk) and have all the parts before you start.
Apple-1 video is probably meant to be a 50 Ohm impedance system, but most monitors are 75 Ohm, and not 50 Ohm (some are). But as long as you keep the video cable shorter than 3...4 feet, you can use any coax cable of any type, 50 Ohm or 75 Ohm characteristic impedance, without seeing any bad consequences of impedance mismatch / reflections on the screen. The numbers given is the length I actually tried out to work fine, and you may be able to use longer video cables if needed (unexpected for a monitor sitting on or near an Apple-1). I prefer to use the thin 50 Ohm Belden video cable for everything as it is much nicer to handle and less stubborn than the thicker 75 Ohm video cables. When we would wire up a video studio, or remote security cameras, different story, then the cables are longer and the impedance matching must be correct. But in our application, we can cheat quite a bit.
Step 1: Cut off two pieces length L of stranded insulated wire of desired color(s). Lmin = 3/4", but 1" < L < 1.5" is recommended as assembly is easier the longer they are, but avoid excessive length as it leads to optical uglyness of the finished cable. Cross section of the conductor should be around AWG20 / 0.5mm^2, but a bit more or less also will work. I used rests of the stranded insulated wire I did use to make the power supply cable. The idea behind use of intermediate wires is, neither be too thin (flimsy) nor too thick (wrecking the contact springs). You can use whatever wire you find that this neither too thin nor too thick. Do not try to wire the coax cable directly to this connector. It is possible, but won't last. Hence, the use of these two intermediate wire pieces. If you happen to ruin one of the contact springs in the connector by a wire being too thick, just swap the springs. They have little locking tabs that just need to be pushed in a bit and then the contact spring comes out. The connector has 4 such contact springs, and you need only two in the finished cable, so you have some spares at hand if things go wrong.
Step 2: Strip insulation for about 3/16" (5mm) on each end, twist strands, pre-tin.
Step 3: Stick the ends into the 4-pin connector, pin 2 (i.e. red), pin 3 (i.e. black, ground) and then use a small diameter punch (or the blunt end of a drill bit etc.) to push the pre-tinned ends down into the slots of the contact springs. If you have a small hammer, you may use that to gently tap on the punch. Do not use brutal force.
Step 4: solder the pre-tinned ends to the contact springs within the connector. Insert the tip of the soldering iron straight from the top avoiding to touch the plastic. The springs alone won't do the job for long, hence, the soldering.
Step 5: De-insulate the coax cable. De-braid and split the shield strands into two bundles and twist each bundle. Twist the de-insulated center conductor. Pre-tin all of that, but avoid overheating the two twisted shield strands: keep the soldering iron away from the inner parts close to the insulation and use the wick action of the twisted strands, and work quickly. The problem is, the insulator of the inner conductor most likely is Polyethylene which melts all too easily. After pre-tin is complete, use a multimeter to check for shorts of shield to inner conductor, which would be bad. Then snip off the worse looking shield wire (of the two just made) at a place close to the outer insulator, but still in a pre-tinned section. Another option is to keep both shield wires, and solder both to the ground wire coming out of the connector, but this is far more difficult to do.
Step 6: Slide a length of thin heat shrink tubing over the ends of each insulated wire coming out of the connector (long enough to cover the exposed metal conductors including the coax) and then solder the coax cable in place. Work quickly to avoid shrinking the heat shrink tubing prematurely. The outcome should look like this:
Note that in the above picture the heat shrink tubing is still loose and not yet shrunken into place, and also note where the shield goes (to the black wire from connector pin #3, counting from the top).
Step 7: Slide the heat shrink tubes in proper position (their only job is to avoid shorts between the center conductor and the shield) and using a heat gun shrink them in place. My result looked like this, which, alas, is not optimum:
It probably would have been better to have the heat shrink tubing on the red wire sit a little bit more to the right to cover half of the center conductor, which would also mean a little piece of exposed center conductor on the left side, where it connects to the red wire, but as long as the two heat shrink tubes are offset positioned such that the shield conductor can never make a short to the center conductor, it is OK.
Step 8: Slide another piece of heat shrink tube of proper diameter over the coax and shrink it in place. Its job is to cover the shield conductor that was still exposed after the previous step, which is inevitable, and to provide some more mechanical robustness. I ran out of proper diameter heat shrink tubing so the piece seen in the next photo is a little bit too short. Still, the resulting video cable is OK and fit for service:
Step 9: Seal the top of the connector with heat melt glue or epoxy glue:
Step 10: Attach whatever connector is necessary to the other end of the coax cable. This may be a chinch type plug or a BNC or a PL-259 or whatever your monitor requires. The first one, in a video context, is a joke because it is never impedance matched to anything, which, because it is dirt cheap, did not deter DVD player or VCR or video game console manufacturers to use it, so many TVs have such an input (typical code color for video is yellow, so it you have to buy one of these chinch type plugs, get the correct yellow color, but any other color will do, if you already have one). The latter two types of plugs have a defined impedance but may be difficult to install for a hobbyist, because most of them used in the industry are of the crimp type, which a typical hobbyist can't do properly. A way out is to buy a complete jumper video cable having the desired connector, and just cut one of the connectors off, and then attach to the 4-pin connector as described above. This also explains why I do not recommend the original Molex connectors for building this video cable: they come in parts, the white shells and loose contact springs, and so far each of my attempts to "crimp" them with the wrong tools lead to a very ugly, inacceptable outcome. And buying the right tools for just making a few video cables is economically infeasable. Each cable would cost me more than $100. This is the crimp connector curse.
If you have an oscilloscope, you may adjust the Apple-1 video output with no monitor connected to be 1.5Vpp (between the lowest voltage in the sync floor and the highest live video voltage). If you have no oscilloscope, just set the R12 "Video Adjust" trim pot on the Apple-1 to the middle position, which should be good enough for most monitors.
Some monitors have a switch to add/remove a termination resistor at the video input. With the Apple-1, put this switch into the "OFF" oder "Hi Z" position. Otherwise, the video signal may get too weak for the monitor.