mpcooper - good for you! i was where you are not too long ago (ie: working hard, decent income, no savings)
You are no doubt going to get a lot of advice. Most of it will be bad (i'll explain why later). Ignore it. Do your own research and come up with your own ideas. If what you do is very similar to the mainstream, you are unlikely to be *very* successful, because you are competing with a lot of other people for the same things. If your ideas are very different from the mainstream, you may be either do very well or very badly, but your odds of doing very well go up.
A short reading list (definitely not mainstream ;)...
"The Black Swan", by Nassim Taleb
"The Speculator's Edge", by Albert Pacelli
"The Book of Investment Wisdom", by Peter Krass
"Hot Commodities" by Jim Rogers
As you will find in the Black Swan, most people greatly underestimate the potential for large moves (in either direction) in the market. In 1987, the market dropped about 30% overnight - ouch. Essentially the market is mostly random short term noise, with some occasional and very hard to predict quantum leaps. The best ten days over the past 20 years account for half of the gains; the worst 10 days account for half of the losses. Whatever you do has to take that into account.
There is a strong consensus today that buy and hold stocks is a way to make money which is faster and safer than other ways ("equities outperform bonds in the long run"), and that mutual funds are a good way to make sure you're not holding the one stock that blows up like enron/worldcom (since such losses would be averaged out in the pool). To see what I mean by strong consensus, heck, we are on a MUTUAL FUND PICKING website. Therefore, being universally agreed upon, that is very unlikely to be true. I have attempted to have as little to do with mutual funds or with holding (long) stocks as possible.
Almost everyone seems to look at things from a relatively short time horizon, and expects trends to just continue linearly. Look at a graph of the Dow Jones for the past century, and also one that zooms in on some of the big crashes: http://en.wikipedia.org/wiki/Dow_Jones_Industrial_Average . Yes, stocks have generally gone up, although there have also been several decades in which they have gone down *a lot*. The past couple of decades have been exceptionally good for most asset classes, and everyone seems to expect that to continue, but that is by no means guaranteed.
In general, the market has "seasons" - in some seasons one thing works and in other seasons another thing. Almost nothing works the same in all seasons. The key is to try to understand what season it is now, and what is likely to work in that season. People were so proud of their stock picking skills during the dot-com boom, not realizing that pretty much all stocks went up - it was impossible to be wrong! As long as you were buying stuff that had anything to do with computers or technology, you made money, like shooting fish in a barrel. That is what worked then, but a few years later it didn't work any more and many people never had the flexibility to switch strategies until too late. Last year was the season to short banks - again, impossible to be wrong, as almost every single bank went down hard. I can't take credit for my stock picking, but I did figure out what season it was reasonably early on.
You have to be very clear on who you are going to make your money from. As Warren Buffett says, "if you're in a poker game and you don't know who's the patsy, you're the patsy". There are two ways of going about this, and they are both speculative, but one much more that the other. You can either (a) try to participate in the overall growth of the economy, in other words have about as average an investment as possible, or (b) try to do the job of a speculator, which is to demand what other people supply (buy what they are desperate to sell - tech stocks in 2003, real estate in a few years) and supply what other people demand (sell what they are desperate to buy - tech stocks in 1999, houses in 2005, soybeans today, possibly oil in a few years). The first way is definitely not "get right quick", so I'm assuming you're interested in the second way.
The stock market is only one vehicle for speculation, and probably not the best one today, since it is much too crowded. Commodities; participating in VC deals; private placement; funding your friends' business ideas; heck, even looking for rare stuff you can buy cheap and sell on ebay all have a better chance of success.
I like what "The Black Swan" calls a "barbell strategy"... keep the bulk of your money in the SAFEST things you can think of (for example: US treasuries, NZ govt bonds, gold in a safety deposit box, interest bearing swiss frank account - or MERKX as far as mutual funds go), and deploy the rest (10% to 30% depending on your risk tolerance) in the RISKIEST ventures you can think of (for example: put options on financial stocks, call options on oil futures, biotech startups, VC deals). Risky here is not a goal by itself (because there are a lot of things that are very risky but offer minimal upside, such as subprime mortgages), rather it is the things that offer huge potential gains and inevitably also happen to be very risky so few people are willing to touch them. I made about 400% in about 5 days shorting AHM (now AHMIQ) with put options last year; I could have just as well lost 100% on that trade (and have lost 50% on many similar trades), but that kind of thing has a favorable risk/reward tradeoff if you do it right. Right now, I have some calls on RIG (down 50%) and puts on BIDU (up 130%), overall result up 15% in a couple of weeks. You get the picture.
The absolute worst thing that can happen to you using that strategy is that you can lose all the money that you have in the risky part; a 20% loss is not that bad. The absolute worst thing that can happen to someone who has their money entirely in the stock market on the long side using buy and hold is, well, let's see, NASDAQ went from 5000 to 1000 recently ;) So the barbell strategy appears to be overall much safer than just holding index funds, even though parts of it are very, very risky.
One more piece of advice... essentially a form of the barbell strategy applied to learning. When you start trading (I refuse to call it "investing" because most of what people do is highly speculative whether they realize it or now, and "investing" sounds too stodgy) you won't have a clue what you're doing. Asking for advice here pretty much proves that - sorry ;) If you keep at it and keep an open mind, you will learn relatively quickly, a few years and you'll be on a roll. The thing is, (a) there is no substitute for trading with real money in real life and (b) you are virtually guaranteed to lose consistently for the first few years. Therefore, set aside a certain small amount of money, enough that you'd care about it but not enough that it'd really hurt you to lose it - $1000 is pretty good - and learn to trade using that. Keep the rest in "safe" things as discussed. At the end of a year, add another $1000 to whatever you have left of yout trading money ;) Again, *try* to make money but realize that you are likely to lose, and don't be particularly upset or surprised if you do lose, just try to learn enough from it that the "tuition" fee is worth it. If you do well, eventually your trading money will become that 10 to 30% of risky capital that a full barbell strategy suggests.