what is no till farming? how do they grow wheat, corn, rice and other plants without pesticides or herbicides?

keeping ahead of the weeds is the big job if one does not use mechanical or chemical weed control. But even with no till there is no complete weed control with herbicides. We eventually have to go back and use tillage, at least shallow tillage to get more complete weed control. Some weeds always seem to survive our herbicide attack, just as some weeds always survive mechanical tillage.
So there is almost no such thing as no-till. It is almost always minimum tillage in reality. But the main concern with tillage is that it causes a large number of seeds to germinate that might have remained undisturbed deep in the ground. One pass with a deep tillage will bring them into action. Which, odd as it may seem is why farmers will deep till late in the fall, but early enough to get weeds growing to freeze off.

When one doe not use any deeper tillage, only as shallow as 2-3 cm deep, we may call that no-till. We are not putting our surface trash into the soil, leaving it as a covering mulch.
Now if we plan to do this shallow cultivation frequently, we can get away with no herbicide and no deep tillage.

Crop rotation coming out of sod is interesting with no-till, no spray. The sod part of rotation is likely to have left a lot of weeds that will persist with shallow cultivation, and one needs a very sharp blade to do the tillage the first time. But it can be done with that sharp blade. One needs a hard surfaced blade to keep it sharp.

For row crop, tillage is usually shallow during the cropping period, so it fits in fairly well. But there is often a bit of hoeing in the rows.

Bugs and disease can be a major temptation to use a pesticide, particularly when the area of concern is small and the area to be protected is very large by comparison. But in that case fire may offer the best solution. However, even with use of fire it will be necessary to resort to biological control, bringing in a predator that will clean up the escapees.
If one catches the infestation early enough, one skips the fire stage and goes directly to biological control.

If the provincial entomologist is involved, it may still be necessary to use fire even after bringing in biological control. Remember that one has neighbors who know you will not be using insecticides and are likely to call for the entomologist to protect their own crops.

With disease, often there may be a soil deficiency that leaves crops susceptible, or this particular crop. But fire again serves to limit the spread as well as does any other method. And in many cases there simply is not a nice chemical solution.

When a mold is involved, often the soil needs something like copper sulphate, and organic farmers may object to using it. They do observe correctly that this happens most frequently on land that has been fertilized with nitrate. This fertilization causes plants to grow faster and use up micro-nutrients like copper and sulfur, or magnesium.

But when one has a field of beans going moldy in a wet fall, there is a big temptation to apply that copper sulphate dust to control the mold right now.  It rarely accomplishes much. so another year they may have used systematic tile draining to avoid having water standing on the surface. That is, they will have to adopt cultural methods that prevent rather than crash methods that may or may not save the crop.

Oh, yes, farmers who do use sprays also adopt many of those same cultural methods too.

No till is just that, planting a crop without any prior tillage.  Some people are able to follow a regular crop rotation while never tilling the soil and using only herbicides to control weeds.  There's fields in my neighborhood that have been strictly no till for over 20 years and have never been tilled in that period of time.  

Other times, one or two crops in a three crop rotation are no-tilled while the third one is.  Around here, in a corn-soybean-wheat rotation, the field is usually tilled after the wheat is harvested and before the corn is planted because the wheat straw keeps the soil too wet for early corn planting.  However, no tilling beans into corn stalks and wheat into bean stubble works great.

Herbicides are necessary to make no till work, but any more herbicides are necessary to make any crop farming feasible.  On the plus side, no till reduces the amount of fuel consumed to plant a crop and also reduces soil erosion, both of which are good for the environment.

Many farmers use no till in my area- NC.  My husband only tills a field when it has been fallow for a long time- such as when he acquires new land.  We also rotate our crops, generally winter wheat, soybeans, and corn.  No till means for us that it is one less step to prepare for planting and we always have to spray anyway throughout the growth process so it really doesn't matter as far as weed control. (with the drought we have been in until just recently we don't have weeds-or beans- to spray anyway.