Well in the simplest form, yes, it can be that easy. Yes you can use JB Weld, but it won't be best and being opaque you likely wouldn't see the cloth very well either. I have been working with CF cloth to repair my racebot and for many other people as well as al kinds of projects. One of my boats is entirely carbon.
Best bet would be to get some 282 carbon cloth, a good laminating epoxy like West Systems, a piece of glass (scratch free, new is best) about 50% bigger than your piece you will be working on, some cheap bristle brushes, neutral (clear) shoe polish, plastic spreaders like for bondo, and lots of rubber gloves.
If you are not familiar with safe practices for any of the materials involved, stop here. Carbon fiber can be deadly, you are carbon based afterall, so your body doesn't reject it if in yor lungs, eyes, skin, or other unpleasant areas.
The glass is going to be your work surface, and the shoe polish is your mold release. Coat the glass with as thin a coat as you can. Spread it on and buff it off with a dry paper towel. Pre cut your CF into the shape or size you want, lay them out somewhere close by. Mix your epoxy according to mfg, I measure by weight and use the two pot method.
Once your epoxy is thoroughly mixed pour some on the glass and spread it outa little bigger than your piece. Lay your first layer down and use the paint bush to help it "wet." Once it is wet take your second piece and lay it on top, and again using your brush to wet it with epoxy, repeat with as many layers as you want. For your first attempt I would take the epoxy and spread it out thin on another flat, preferably disposable surface like a pizza box. It will help dissipate the heat extending pot life.
For structural applications, alternating cloth orientation 45* helps tremendously. When doing a wet lay-up, it is very easy to get too much epoxy in the laminate. You want the least amount possible. When it comes to pressure there are a couple different ways; weight piled on top, clamps, or vacuum. I don't like using weights, as it usually has to be balanced, clamps are a good way, and I include any mechanical squishing, crushing, clamping, or squeezing in the catagory. It is what I use mostly.
Vacuum is the best method, also it can be quite lengthy to explain here, I have heard of people using "food savers" type vacuum sealing machines. If the part is small enough just place the whole thing in the bag and proceed to draw all the air out. On the glass, you would have to get a roll or two of seam sealant.
Frank is right, if you don't already have many of the materials it can be very expensive to make. Workin it can pose some challenges as well. "The rash," is a bitch, so suit up and use good respirators and dust collection.
Its getting late, and I am a little out of it, if you need more info let me know.
-Xander