Were the weeds annuals or perennials? If they were perennials, they will be back and you need to get them controlled before planting a garden in that spot, else you will be fighting them for years. If the weeds were annuals and were that big, just the cutting will kill many of them, and you can go after the rest with a rototiller getting the ground ready to plant.

No idea what you read about Round-up, but make sure it is from a reputable source and not a Round-up-hater. If you spray the weeds with glyphosate, keep your critters leashed for 24 hours and they will be fine. Just waiting for it to dry is long enough, but 24 hours will give you plenty of margin. Glyphosate adheres strongly to dirt particles and loses its toxicity to plants at that point. Many farms spray a field with glyphosate in early spring to get early weeds, then plant a few days later. No toxicity to the crop at all. It will take some time for microbes to break 100% of the glyphosate down into water, carbon dioxide, etc. (hence maybe the 3 year figure is for 100% disappearance), but once it is on the soil particles, you have nothing to worry about with your garden--the glyphosate is totally inactive.

I wouldn't worry about spraying at all, just keep them under control, but no need to eradicate.

Here is a link that might be useful: Weeds: Guardians of the soil

I wouldn't recommend using any weedkiller or chemicals at all. My suggestion is to use newspaper to cover the soil in all areas possible. Use straw, grass-clippings, whatever you have handy to hold the newspaper down. This has been very effective for me. I also recommend that you do this at the time that you plant your seeds or set out your plants. I have come to the conclusion that the extra time spent at planting time to take this extra step is well worth the effort. For the areas around and between your plants just pull the weeds by hand or by carefully using a hoe.
Good luck and hope this helps, here's to many successful weedfree gardens!

As was already suggested, round-up on a sunny day will dry fast and have no ill effect on the animals once dry. And you can plant very soon afterwards.

Is it your intention to make the entire yard into garden or do you want some lawn for your critters to play on? If you plan a lawn, will you seed or lay sod? Personally, I think in either case getting the weeds dead before planting grass is absolutely necessary. Tilling is not an option around the roots of the flowering trees, but a light mist of round-up right to the leaves of the weeds will kill them quick with no harm to the trees.

Sure, there are other options, but you did mention that you want a garden THIS year. And that is one thing. You can dig up a small area and hand weed for a garden in no time. But if you would also like a lawn this year, with minimal work and cost, you might reconsider.

Kay

I use Round up in my garden every early spring to deal with the crop of winter weeds that invariably find their way in - henbit, chickweed, etc. Tried just tilling them once, but it just chopped them into smaller pieces and replanted them - had more than I started with. Been using the round up this way for several years.

Mulching weeds with a thick layer of recycled cardboard and newspaper topped with topsoil, shredded garden prunings, and bark worked for us on a near-acre sized garden. It took some time to mulch that large a space--so we anchored the cardboard with topsoil to start. This was on an area that had never grown anything but weeds and we eliminated 80 percent of our perennial weeds the first year. We planted a small vegetable garden the first year and then expanded each year continuing to sheet compost with a bottom layer of cardboard. On a large garden several years ago we used a gas-powered flame weeder (at the end of the rainy season before the countryside dried for the season).

Here is a link that might be useful: HarvestToTable.com

I would stay away from roundup.
Don't forget, the people that made it, also made agent orange.

I used roundup, than a layer of cardboard and finally soil in my raised beds. Or Bermuda grass would keep coming back and back and back.

Cook them with clear plastic next winter.
It ALWAYS works for me.

Without knowing what kind of weeds we are talking about it is hard to say just how it spreads, by seed, by rhizome,or both. Know thy enemy.

I have had good luck pulling out the roots of many of my weeds. Learn to identifiy the weed and start early in the spring. Once you recognize the plant at each stage and know how it spreads you can make remarkable progress. In a year you will have the target under control and will be concentrating on a new target.

Of course you will also have to use some of the other methods mentioned. Deprive all the weeds of sun by using mulch, newspaper, and cardboard to smother them. I use roofing shingles on the tough ones and just keep moving them around.

Wait til the soil warms then put down the newspaper or cardboard. Cover with mulch to give it a better appearance. I like this cuz unlike the landscape fabric both will decompose and add organic matter to the soil.

If they have seeds when you pull them bag em and discard. I use the shopping bags to contain them until they are dispatched off site.

Unless you can HOT compost you will only spread them if you add weed seeds to your compost pile. So I would avoid this.

Consider using corn gluten meal for the billions of seeds you will miss. Timing is the key with CGM. It needs to be applied before the forsynthias bloom and again in mid-summer.

Corn meal gluten interferes with normal seed sprouting. It will keep many weed seeds from growing. However, if you plan to sow vegetable seeds in your garden, it will eliminate their growth, also. If you plan to use all transplants in your garden the corn meal gluten would be a possibility for weed control since it does not affect older plants....be they weeds or desired veggies. It also will not stop large underground roots from weeds from resprouting. It is effective only in stopping seedling growth.

The cardboard thing always works for me, but with cardboard on the first year you will be limited to planting large plants (such as tomatoes, no carrots or other direct seeded veggie), punching holes through the cardboard. I have a garden knife specifically for that purpose (punching holes in cardboard).

I suggest cardboard this year (go to the nearest recycling center and load up). To hold it down, put down some mulch, I suggest of a type that will be gone in a few months, such as grass clippings (or even the weeds you just whacked, if they have not set seeds yet). In 3 months, carboard and mulch will be gone.

The cardboard will kill the existing weeds and allow you one season of gardening but it will do nothing for the seed bank. You may have, say, a very persistent bramble survive three months under cardboard. For that, do buy Roundup and a small paintbrush. Paint a few leaves of the bramble with straight Roundup. This will not poison anyone and be extremely effective. I have a 1999 Roundup bottle which I use only this way. It lasts forever, of course.

Now you have to worry about the seed bank. Solarization is best, as others have suggested. You can solarize half a garden while you garden in the other (mulched) half. Do solarization right: hermetically sealed edges, lots of watering, plenty of time, some light hoeing midway. In fact, I prefer to always add mulch, and when it becomes soil, it is weed free. You need to add lots of it because typically one foot of mulch becomes one inch of soil.

In areas of the garden that I don't want to use chemicals, I sometimes use hot water. It works pretty good if you let it soak into the ground deep enough and it gets the roots hot enough to kill them. During the summer, I leave my water hose laying out in the yard and the water thats in the hose gets very hot. I spray that water on the occasional weed while I wait for cooler water to come out for my veggies. The more hose that lays in the sun, the more hot water for killing weeds. I've also used water that has been heated on the stove. Water left in the pot from water bath canning is taken outside and used around the edges of the garden to help keep bermuda grass at bay. I've even considered hooking a hose up to my hot water tank to kill larger areas of grass and weeds but I havent done that. I hit on the idea of using hot water one summer when I killed a 5' diameter circle of my bermuda lawn with hot water from my hose. It took months to get that spot filled back in with grass.

I heartily second the solarization advice (covering with plastic, making sure to water the area beforehand and seal the edges of the plastic well, and cooking them). This will not only kill all the sprouted weeds including bermuda grass, but will also kill the vast majority of any weed seeds. The only things this won't kill are plants that can sprout a long distance away from a "mother clump", such as bamboo and (I think) bindweed.

The only negative side effects solarization has is an upset in the soil flora and fauna, but if you add compost and molasses when you till afterwards, this is completely reversed in no time.