Hello world! I have little experience in CAD, and I have to design a mount for the radial bearing 217-3246. Please help!
It’s hard to help without a little more detail. What is the application for which the bearing is used? What are the requirements for the mount?
Here’s some ideas to get you started. https://www.sparkfun.com/categories/261
This is a pretty general overview of bearing mounts, hopefully it’s somewhat helpful. If you would like some more targeted advice, some clarification on your specific project and CAD experience would definitely help 
The context of the overall design is important.
Does it need to be able to slide for tensioning purposes? Then a bearing block set in a channel is probably what you would want to design, or grab a predesigned one off the internet (to purchase later, if needed). Tensioning systems are a pain to manufacture and design, and require a lot of extra parts, so this usually only applies to drive trains. 
Otherwise, mounting a bearing is pretty simple, and there are a lot of options. It can be made with sufficiently large aluminum extrusion, machined out of a block of metal, plate, or really sturdy angle brackets. Attachment methods could include bolts, pop-rivets or welds, depending your resources.
The main requirement for placing a bearing is a sturdy place to bore a hole that fits the outer diameter of the bearing (main body, not the flange). If the supporting material is thick enough, and the bearing happens to have a flange, you can add a countersink so that the flange does not protrude from the surface of the mount. Generally, it’s also good to have two support points for each shaft, so there will be another bearing or a gearbox that shares the shaft. If there is a flange, it is usually easier to put it on the “outside” of the pair of supports.
In terms of CAD, what are you familiar with, and which modeling program do you use? It’s possible to design many parts using just basic sketch tools, and extrude or rotate to add and remove material.
This particular Vex bearing is an industry standard R3 size, available at lots of other vendors as well. If you want an non-Flanged sealed bearing it’s a R3zz.
The Flanged version is a FR3zz. If you drop the zz suffix they are open bearings.
3/16 is a fairly small shaft size, be careful with the loads applied on that in your design.
I need to mount the bearing on a bracket so that it can roll along length-wise along the bar. My problem is that I don’t know how to CAD a suitable mount for the specified bearing.
What type of bearing might work if the load was to be approximately 15 lbs. distributed across 4 bearings?
Are you attempting to restrain a shaft moving lengthwise rather than in rotation?
There are both bushing and linear bearings that are suitable for this type of usage. Standard rotational bearings will not work.
You might look at McMaster Carr to get an idea of what is available and how you might mount them, search for “linear bearings”
IGUS (First Sponsor) has the Drylin R line that’s worth looking at. (They give a discount for all First Team orders. Really first rate products and customer service in my experience.)
I’m trying to use the bearing as a wheel.
If that’s the case, why not just use a caster or something similar? It won’t be driven anyway.
An igus bearing will work, though.
Perhaps shoulder bolts will help
http://www.mcmaster.com/#shoulder-bolts/=zxuxzw
This, or, possibly, just a regular bolt. Sounds like you’re in a pretty low-stress environment. The main thing I’d just point out is that bearings aren’t designed to go over rough terrain, so you might want to avoid off-roading. A bolt and a bearing is probably fine (though a little sketchy) for light use.
I can’t really tell from your descriptions and pictures, but are you trying to move something linearly along / inside an extrusion, like an elevator? In these cases, you’ll need multiple bearings / bearing surfaces and can accomplish their mounting with two plates and a bolt going through both of them. It’s a lot harder to do it inside of a tube compared to the bearings riding on the outside of a tube. Perhaps I’m not understanding you well.