Those Gardens!

Newspaper

A simple, inexpensive, and organic way of controlling weeds is to use newspaper. Cover the area you wish to rid of weeds with several layers of newspaper, then spread mulch or compost over the newspaper. You can plant whatever you would like over this. Just poke a hole in the newspaper for the seed/plant and plant away!

A good reference would be Organic Gardening magazine, published by Rodale Press. They also have a website: OrganicGardening.com. They have a lot of good inexpensive organic tips and can point you towards other references, such as square-foot gardening and other labor-saving and organic methods of gardening. Organic is better for you and for the environment.
Tracy H.

Depends on Your Goal

Weed control can be difficult and simple. If you don't want to plant anything in the area get rock salt and laden the area with salt, the only problem is that you will probably never be able to plant anything there for a very long time.

If you want to plant, a time consuming method is to water the area prior to the growing season cover the are with black plastic and let solar energy do the work. The weeds will sprout but will die do to lack of sunlight. The problem here is that as you disturb the soil for planting you disturb weed seeds, so you may need to kill the weeds, till the soil, kill the weeds, etc.

Another method is to cover the area with a weed barrier and import composted soil (but this is not cheap).

I hand weed, till, plant, use Round-Up and hand weed. If you have well composted soil weeds are easy to pull.
DG in Albuquerque, NM

Killer Salt

If there is an area where you don't want *anything* growing back, salt water is a great way to kill off weeds and keep them from coming back. I use 1 part salt to 2 parts water.
Anne P.

Cheaper Cost for Round-Up

Concerning how to get rid of weeds & grass other than using Round-up, what do you want to use the area for? If you want to replant in the area, you'd be hard pressed to find a product that works both as well as Roundup, but also that has *no* carry-over for future items planted. No, I don't sell it, but my father (farmer) has used it since it came on the market, I used to use it to hand spray large thorn weed patches in the pastures, it doesn't adversely effect animals/etc. I believe the patent recently expired, so perhaps there are now Round-up equivalent product available. If you go with Roundup, definitely buy the concentrate; the pre-mixed means you pay a lot for water. Prior to Roundup, we had to spray a lot of nasty stuff to clear a field between rotating crops, which wouldn't neutralize when it interacted with the soil (like Roundup does.) Pricey, yes, but very environmentally friendly to compared to alternatives.
Roger

Vinegar and Dish Soap

Weed control is very difficult to get under control but there are a few ways to do it.One is to make a very strong vinegar and liquid dish soap mixture and apply liberally but locally to the weeds,also gasoline sparingly but locally is a excellent solution.
Iain

Buy Bulk

I do not know where you live but I needed to kill a large area of weeds and found Round-up very expensive so I did some research. 1 quart of the 41% super concentrate costs about $80. If you buy it at a farmers supply house for agricultural purposes it costs $150 for 2.5 gallons. I still thought this was expensive so I contacted a farm supply co-op in Canada and found out that the patent has been off in Canada for a few years and the price is even less. In Canada it cost me $100 CDN ($65 US) for 10 litres which is even more than 2.5 gallons. I got together with my neighbor and bought one and split it the first time and it lasted me quite a while. This last time I bought an entire jug for myself. I have tried many other products through the years just because of the cost of Round-up and always ended up disappointed. Round-up has worked the best.
Robert L.

And Stay Out

After weeds are dead, do not rototill! Every time you rototill, weed seeds are brought to the surface to germinate. Some weed seeds can lay dormant FOR YEARS until the right conditions exist. Rototilling is highly overrated. Not only does it provide a medim for weed germination, but it destroys the soil structure. Soil SHOULD be naturally layered.
from a Master Gardener in NY

Tarp Solution

A very effective and cheap method to completely eliminate grass and weeds is to cover the area with a plastic tarp for several weeks. Weeds and grass need sunlight to survive, and will die if deprived of the sun.
TS

As Cheap as Water

I use a kettle of boiling water to kill the weeds that grow in the cracks of our sidewalk. I just pour it on the weeds (especially at the root) every day till they die. works pretty good and is safe for kids and pets after treatment.
Melissa W.