I think the honest answer is it depends on the teenager and their interests and abilities as well as access to startup funds. A couple of low-cost options:

Lawn mowing business. Dependent on them having a ute, or car with a trailer. Fairly low startup cost, they just need to buy a lawn mower and a whipper snipper, maybe a few other things. Base your rate on an hourly rate, work out roughly how long it might take you to mow a particular lawn, then just do fixed-cost for that lawn. You'd be competing with Jims etc, but it's an option.

Car wash/window wash. While not really a business, when I was much younger I used to spend time at the small local shopping center, offering to wash car windows for $1.00 while people were shopping. Maybe as a teenager you'd want to charge a bit more though.

As the second poster mentioned - become a reseller or dropshipper and sell things on ebay? Dropshipping - where you as the business don't actually own and hold the things you're selling, but the supplier delivers them direct to te end-purchaser, with your branding.

If they're into art or craft, they could make their own art, or photo prints, or handmade things and put them up on an Etsy store.

Or they could put up signs or flyers around their neighbourhood and offer tutorials to older people on how to perform basic tasks on their computers, like email, and searching on the internet, or even showing people how to use their mobile phones and set top boxes. Stuff that is natural to kids, but that some middle aged and elderly people may not have caught up with yet.

Or the traditional gardening help, flyer dropping, and so forth.

There are also a lot of sites popping up where you can register to do tasks, like O-Desk, Fiverr, Sidekicker, Airtasker, and so forth. People post odd jobs, admin tasks, and web projects for a certain fee, for people to complete.

Depends on how creative and enterprising the kid is. Sky's the limit. They could learn to code, and build the next big app!

It's not been made public yet but Telecube is building a prepaid wholesale telecoms system which will allow anyone to become a telco overnight.

It will be possible to sell 1300 numbers and VoIP services with a fully rebranded online platform.

Anyone with an interest in internet technologies or telecommunications will be well suited to this industry and there will be no setup costs or ongoing charges to participate.

Anyone interested can call 132823 and ask for info.