Well,
We got the property we are on (about 5 acres) when I was broke, out of work, and in debt. Had already sold most everything we had of value just to scrape by, and that ran out as well.
We started doing this grow food thing out of necessity, while still broke. It didn't work well without investment money for some very basic tools, one of those ended up being our John Deere 316, and them adding a 3 point hitch, better tires, attachments, etc. It was possible without, but insane amounts of hard, manual, time consuming work can be eliminated with the proper tools.
Now, here is what you will find interesting: You really don't save money growing most types of veggies if you are the average person. Why? Veggies are cheap to buy. That said, we eat organically (exclusively), and some veggies are VERY expensive to buy organically, ironically many of which are easy to grow (like potatoes).
Where we save real money is protein production: eggs, meat, dairy (dairy is in the works, that takes time to get going). Dozen organic eggs in the store is about $5. I can produce them for about 70 cents, if that. Organic chicken is very difficult to find, and $9/pound when you do (I can raise meat birds organically for $6/bird if I buy all their feed, and buy chicks, $4/bird when I hatch my own chicks, and I haven't started fodder yet). Organic dairy is stupid expensive (we pay $8-$9 for a gallon of milk), and even buying beef/pork from the farmer by the animal (which IS cheaper than grocery store prices overall) meat gets REALLY expensive.
As such, we decided that next year our gardening would dramatically change.
We are going to concentrate on perennial food such as berries, fruit trees, etc., high value and un-available veggies, and feed for the animals. We are getting a greenhouse this fall, and are going to have it setup for next year. This will allow us to get about double the amount of crops off the same square footage of land. This will be for the "people" food, and the open garden areas will be for animal food production.
So, back on track..
Can you do it? Yes. Does it take a lot of money? Depends on what you call a lot, and if not, it takes a LOT of manpower. Can you live off the land only? Not in this country. You will ALWAYS need to generate income, at least at SOME level, if nothing to pay taxes on your land.
So, what do we have in turning our 5 acres into a mini homestead? Without going all spreadsheet, I'd say the cost of building everything from scratch, but with salvaged components where available, buying animals, tools & supplies to be somewhere around $5k. Our property was $40k (it was an amazing deal, long story, but stupid cheap for around here). Now, I do have access to a skidsteer from the farm, which I bring out a few times a year to get certain projects done that I cannot do with what I have for equipment, but you can also rent them, which can be easily cheaper than buying for just a few projects a year.
We STILL aren't wealthy by any means, and STILL haven't gotten our investment back yet (we really started investing in this about 3 years ago), but next year should get a long way toward recouping our investment as the cows will be in lactation, the pigs will be brought in, the meat birds are actually going to break even (considering the cost of the coops).
Let me know if there is anything specific you have questions on.
Also, more info can be had at the website in my sig line (still a work in progress)