Question: My new Canon EF 75-300mm telephoto lens and the zoom ring is quite stiff. Is the lens faulty or is there a way to loosen it up?

Answer: 
I had similar sounding problem with an ef 75-300 I bought about a year ago,
It felt almost as if the outer casing of the barrel was rubbing or catching in places against the inner making the movement feel a bit jerky!  

over time however using the zoom ring seems to have become a more fluent action, 
the front focusing ring is soft and smooth but it always was so,
I suggest if the lens is still covered by warranty that you contact your supplier and discuss your concerns!
regards
M
**Background:** This might seem more a non-answer, but I am recounting from personal experience. Faced with a fogged lens due to continued shooting in extremely muggy Florida weather in summer, I took it upon myself that as a mechanical engineer, I could fix anything, especially as I was quite impatient. 

I disassembled the lens and could never put it back. Relenting to buy a new lens at Naples I was told by the store people very clearly that LASER is used to assemble lenses, so they told me never to try that again! 

After a while I looked and the damaged lens's fogging had gone away by itself. Patience would have been the best fix in that case. 

Pay attention to what "mattdm" has suggested and simply call the store/dealer that sold you the lens, find out if you have warranty and try to get it fixed. 

Another reason why you may want to stay away from fixing things yourself is, there wasn't a particular incident that caused your lens ring to tighten, so it might be a manufacturing defect from the get go.