How bad is this?

It depends.

• On what is causing the haze and how bad it currently is. The cause could be as varied as: fungus, lens separation (the glue holding elements together hardening and letting go), high amounts of dust inside the lens, etc.
• The cause will also determine if it is reversible, stable, or only going to get worse.
• On what your intended use for the lens is. Haze reduces contrast. When shooting into backlight or with strong lighting sources on the periphery it produces vieling flare. Sometimes flare is desired. Usually it is not. In other situations light haze may not have any noticeable effect on the resulting photo.

How cheaply it may be fixed.

You almost certainly would not want to spend more to fix it than a more pristine copy of the lens is worth.

Again, it all depends on the lens. Obviously one can spend several hundred dollars getting a $1,000+ lens cleaned internally cheaper than buying a new one. On the other hand, a $200-300 lens is cheaper to replace than to have disassembled, cleaned, and reassembled.

If fungus has not etched the glass, it can be killed without opening the lens up by exposing the fungus to UV light. To remove the existing haze, though, requires opening up the lens and cleaning it. If the fungus has etched the glass, the damage to the glass is not repairable short of replacing the lens element(s) in question.

If lens elements glued together are separating the elements in question must be removed, cleaned, reglued, and the lens reassembled. Probably not worth the cost unless it is a lens worth close to or more than $1,000.

If a lens is full of dust to the point it is affecting image quality it probably needs to be totally disassembled and cleaned.

Unless you know what you are doing, have the proper tools and diagnostic equipment, and know how to optically adjust lens elements and measure the results as you reassemble the lens, then taking the lens apart and cleaning it yourself will probably make it totally unusable. Once you take it apart yourself almost no repair shop will put it back together for you. Even if they do, they'll usually charge more because it is harder and more time consuming to put together a lens you haven't disassembled.

Some lenses can be partially disassembled enough to clean certain elements without necessitating involved measuring and adjustment when reassembling, just be sure to mark positions of adjustments and shims as the lens is taken apart. That is totally dependent upon each lens' particular design and where in the lens the cause of the haze is located, so you'll need to search for instructions on how to do that on a lens-by-lens basis.

Take for example, the Canon EF 100-300mm f/5.6 L you mentioned in the question. Very good copies from reputable used dealers can be had for around $300. It's probably not worth it to try and get a better price by accepting a lens with haze. Just getting anyone to open the lens up will probably cost more than $300. Canon factory service won't even service that lens. It has been out of production since it was supplanted by the EF 100-400mm f/4.5-5.6 L IS in 1998. Canon generally supports lenses for seven years after they are discontinued.