Writer's Market is the standard publication for finding these; ideally, Novel and Short Story Writer's Market, as it is more focused on pertinent interests. It's published annually (in autumn, I believe); if you can't find the current year, find a recent one and go to the websites of the publication you want to sell to, as contact information (and often other details) change with great regularity.
Yes, there are quite a few magazines out there, though at this point many smaller publications have switched to internet-only. Unfortunately, finding paying ones is somewhat trickier… the previously unpublished should generally not worry about this, concentrating instead on getting some publication credits that can be put on a cover letter to help convince editors of more prestigious markets that there really are people out there reading your work.… Besides, you're never going to get rich writing fantasy shorts anyway. The premier market, in terms of pay and circulation, is Magazine of Fantasy and Science Fiction; second is probably Weird Tales, though as the name suggests its wants are somewhat narrower than "fantasy" writ large. Be aware that in submitting to any comparatively "large" market such as these, you'll be up against tremendous competition… another reason to start small.
Beyond those two, you just need to slog through the various listings in the Market books (there are indexes to help narrow your search). Read the magazines' entries carefully before submitting, though: a great many markets that say they accept "fantasy" aren't really all that interested in it, and/or won't be read by your target audience. If you aren't familiar with the mag, further research is probably indicated–and note that the most common piece of advice on determining a mag's needs is to obtain a sample copy and see what they're actually accepting, as opposed to what they'll "consider."
Getting a short story published involves sending it to LOTS of markets. Writer's Market will have a list of the premier (and perhaps some second-tier) publications. There are plenty more directories online, but you'll often need to sift through them to find out which markets are still active, as there is a high turn-over.
Critters is a workshop geared towards short story writers. The page I've linked is their home page, but from there you can find links to a decent market directory (my above advice about 'checking for active' still applies, though).
The SFWA website has some links for short story markets. Most of them seem pretty good and you actually get paid. I was hoping to join them in the future, because they help out with lots of different things.
I'm supposed to be in an upcoming anthology that includes Michael Moorcock, so that's pretty cool. Still waiting to hear the final word on that. Anthologies seem to mostly solicit people or get people they know are reliable. The other time I was solicited was by a professor who had read my poetry and liked it, so he asked me to write a new one for an anthology he was working on.
I've joined the local writers centres, which either have a website or newsletter or both, and they keep me informed with everything that's going on. And I follow my favourite publishers on facebook and twitter, and they update me too. And there's a group called the Australian Science Fiction and Fantasy Writer's Association, who often tell everyone of what's going on in the scene.
Joining a few places like that should ensure you hear of everything and anything
I would start with the SFWA list and end with Duotrope. With the internet, you're basically wasting money on Writer's Market for most writing careers (unless you're buying it for the articles...). You can find listings of the reliable (and even the tiny, not so reliable) publishers out there for free without paying for it. Plus the listings tend to be more up to date and more reliable online...