Although my opinions don't necessarily represent those of other (far better) jig fisherman on this site, I thought a post like this would be beneficial to many. The information I'm presenting is not the only way to get started into jig fishing, but it is a way that has been working for me since I started fishing jigs.
Step One: Equipment
In order to start fishing jigs, you need some jigs (duh!), trailers, and something to throw them on.
Jigs and Trailers:
The Jigs:
I'm a big advocate of simplicity in jig fishing, and so I'm starting you off with some basic, proven jigs.
I'd recommend a 3/8 oz. casting jig (you might also hear it as an arky head). You're looking for a streamlined head that will go through cover easily.
3/8s of an ounce is a great weight to start out with. Later on you may want to try heavier or lighter jigs, but the 3/8s is a great size to start with. This jig is very, very versatile and can be hopped, dragged, swum, and fished in all types of cover.
The Colors:
Again, I'm keeping it simple here. I'd recommend two colors of jigs: one of them being Black & Blue and the other being Green Pumpkin. While there are many, many other colors out there that work and perhaps look cooler, these ones will get the the job done for you. Many experienced jig fisherman primarily use these two colors, and they're a great way to go whether you're starting out or have been fishing jigs for a long time. Note: When I say, "Green Pumpkin," I'm' referring to jigs are primarily green pumpkin, regardless of other colors mixed in, such as purple, red, black, or blue. Fish the Green Pumpkin jig in clear to semi-stained water, and fish the Black & Blue Jig in stained, dirty, or muddy water.
The Trailers:
I'd recommend the same colors for trailers as I did jigs. The trailer I use 99% of the time on my jigs is a Strike King Rage Chunk. There are many other trailers out there, but the one I'd recommend is a Strike King Rage Chunk (or craw). If you're on a budget, I would recommend picking up some NetBait Paca Chunks, which work pretty well. Otherwise, do yourself a favour and buy some Rage Craw Chunks.
The Combo:
Rod:
I'd recommend a Medium-Heavy baitcasting rod. Some people prefer a Heavy action, but I like a Medium Heavy. There are many choices of rod companies out there, so find one that you like. Just make sure you get the best one you can afford. Jigs can be fished on any rod, but they're easier to fish on a sensitive one.
Reel:
Again, many options are out there regarding reels. Couple things to keep in mind: Make sure you get one that has a decent gear ratio (I like a 6:4:1 or higher). And while I believe that the rod is much more important, it's also wise to get a nice reel for your jig combo.
Line:
I really believe in throwing my jigs on braid with a leader, but I seem to be in the minority on this, as many jig fisherman like fluorocarbon. I'd recommend 30 lb. braid or 15-17 pound fluorocarbon. The reason I like braid is that it allows me to get a good hookset on a long cast, but fluorocarbon also does a good job.
Step Two: Research
I cannot recommend highly enough that you do some reading on BassResource, particularly the first thread I linked to: http://www.bassresource.com/bass-fishing-forums/topic/12403-jig-fishing-questions/ http://www.bassresource.com/fish/jigs.html http://www.bassresource.com/fishing/how-to-fish-jigs.html http://www.bassresource.com/fishing/jig-fishing-specifics.html http://www.bassresource.com/fishing/bass_fishing_jigs.html
Step Three: Go Fishing
Many people will recommend that you go out and throw nothing but jigs until you start seeing some rewards, but this can also be very frustrating. While jigs are some of the most versatile baits on the market, the bass don't always want them. My recommendation is to gain confidence in fishing soft plastics and especially texas rigs first, and then to go out and throw jigs in places where you know there are bass.
I hope this helps you get started in jig fishing. Other people on here will have far better advice than I do, so make sure you read the comments and see what they have to say when they chime in.
Good luck!
P.S. If you're looking for some jigs to start with, I highly recommend checking out Siebert Outdoors. Mike Siebert has sponsored these forums for a long time and makes some quality jigs.