Well, the easiest way is to save up you money and buy the monitors, but....
What you need to do is use what you have (headphones, computer speakers or hifi speakers) to do a mix then burn a CD (or make a good quality MP3) and play it everywhere you can think of--in your car, in your iPod, on a friend's hifi, etc. etc. and see how it sounds on lots of different systems. If you're really lucky maybe it'll sound good but, more likely, you'll decide you need more/less bass, more level on the vocals or whatever.
When you've decided what you think would be better, go back and re-mix it to try and achieve the "better sound". Repeat all this several times
Do this a few times and you'll gradually teach your ears what a good mix sounds like on whatever headphones/speakers you have available to mix on.
(If it makes you feel any better, even with monitors worth thousands, you still have to "teach" your ears how to use them to get the best.)
Hope this helps,