That depends on what companies you want to short and your broker. I've shorted plenty where I just had to enter a few numbers and press a button...
There's also any number of companies that let you do the equivalent via CFD's (Contract For Difference). Be warned: Many of them allow crazy levels of leverage that can wipe you out with tiny little swings.
You're right it's not a given that you'll be able to "just" short whichever share you want, but it's hardly difficult to find a way of betting against a given company.