You can look for a CSA in your area, http://en.wikipedia.org/wiki/Community-supported_agriculture : CSAs consist of a system of weekly delivery or pick-up of vegetables and fruit in a vegetable box scheme, sometimes including dairy products and meat.
You can use http://www.localharvest.org/csa/ to try to find one in your area.
cooking.stackexchange.com/users/264/Nick Canzoneri
I've had friends and family go in on "buying a cow" from a farm.
You order a whole cow from them, they will get it butchered and you get all the various cuts from it, ground beef, etc.
You can do it yourself and fill up a big chest freezer and thaw as you go.
If you have other people in your area interested, you could always buy together, divide up the goods and that way be able to order more frequently with less freezer usage.
Here is an article about it hitting on some good points http://www.culinate.com/articles/culinate8/cow_sharing
cooking.stackexchange.com/users/203/ManiacZX
Similar to @Nick's CSA suggestion , I've got friends who formed a (sort of) food conglomerate.
It needs to be a decent size (4 - 8 families).
Once a week, one family goes to the wholesale markets and buys the fruit & veg for all families.
Its one of those things where it is financially cheaper, but time and resource expensive.
(8 families of fruit is a lot of apples and wont fit on your backseat)
Once you have your routine down, it is very effective!
cooking.stackexchange.com/users/113/Christian Payne
Just taking the "produce" part of your question, what about growing your own?
Even if you don't have a lot of garden most sources of advice for novice gardeners will talk about how to make the most of even limited space.
Foodies & cooks will want to focus on: a) produce which tastes substantially better homegrown e.g.: tomatoes (especially) strawberries cucumbers
peas b) produce which is expensive and/or stores badly, so that having a fresh and abundant supply outside the kitchen door is really a cook's delight e.g.: herbs lettuce rocket beans
For these reasons I tend not to bother too much with cabbage, leeks, potatoes, onions, courgettes (arguably) etc
all of which are cheap and store well and taste decent from the shops.
But I got into an argument the other day with someone who reckoned I had onions completely wrong and didn't I know homegrown onions were divine.
So I could be wrong.
cooking.stackexchange.com/users/373/Tea Drinker
Really, a Farmer's Market is your best choice.
You need to start going there more than "occasionally" :)
You have full control on what you are getting (unlike a CSA), you can taste the same produce (e.g. a Peach) sold by different vendors and decide who has the best tasting one, etc.
etc.
@hobodave, your profile says "Chicago, IL" -- here is a website I found with a list of Farmer's markets in Chicago: http://www.explorechicago.org/city/en/things_see_do/event_landing/special_events/mose/chicago_farmers_market.html
cooking.stackexchange.com/users/470/joyjit
I often go to Whole Foods, but I feel like I'm getting ripped off there. I can walk out having spent $120 on a single bag of groceries. I try to get to a Farmer's Market occasionally, but not often enough I guess.  Are there other ways to buy as close to the farm as possible?
What methods are there of getting fresh local meat & produce?
cooking.stackexchange.com
<meat><produce>
cooking.stackexchange.com/questions/1844
cooking.stackexchange.com/users/60/hobodave
Some community options exist like a weekly fruit and vegetable box delivery or sharing bulk purchases of fruit and vegetables or even a cow from a farm. A farmer's market in your area is a good option. You can also consider growing your own produce. While a Farmer's Market is your best all round option, you can look for individual farmers who have delivery or pick up schemes. Another option would be to team up with other families or try growing your own.
Look for a weekly deliver or pick up system from a local farm in your area. You could team up with other people in your area and buy local produce together to reduce prices. Try growing your own vegetables. A Farmer's Market is your best option.