basic reqirements:
1) love kids
2) previous experience, even just spending a few hours on different occasions with younger children/siblings/cousins/neighbours/etc...so you know how to react to kids, games to play, etc.
3) they like you to have your own (hopefully fairly reliable) transport (own, public, lifts from your folks, etc), as its one less thing that can go wrong..and they dont have to worry about taking you home/picking you up (though i havent had anyone complain that i dont have my licence)
i've done a tonne of babysitting (paid and unpaid) since i was pretty young. started by helping to look after/spending a bit of time playing with younger cousins, and then gradually built it up with neighbours, etc. most of my paid work has been in the last 3-4 years, and the jobs were through word of mouth.
put out flyers over the place - shopping centres, letter box drops (if you know of areas with young kids), give some to rellies/friends/neighbours to hand out, possibly at some local preschools (worth a try), etc. remember to specify what age you prefer to work with.
try to be as flexible as you can...most of my work comes on thurs-sun nights and weekend days, though you can get some more regular work earlier on in the week for working parents (my regular one is 9-5 every tues & thurs). note, regular jobs (ie. set days, every week) will be more likely to ask for a resume..so try to look for casual jobs first and build yourself up
you should try to have a general idea of how much you want to charge (work around 1 kid/hr). i usually work with parents on what they think is reasonable (numbers, ages, hours, time of day, responsibilities, etc)...this' good to get an idea of a reasonable price for you, but if you have a 'base rate' that you can work with its' much easier. personally i'd be aiming at a base of 1 kid, $10-12/hr...any less and you're generally ripping yourself off, too much more and parents wont want to pay it.
when you actually get people calling you for work, ensure you have their details correct (name, address, contact no), time and date confirmed, and try to arrange for a few hours to get to know the kids, the parents, their house, etc (dont ask for payment for this time, but still why refuse it if they offer lol).
good luck. its not the easiest of industries to get your foot in the door, but its great when you know what you're doing
pm me if you want any help..i'm almost a professional babysitter (minus the abn)