Sometimes a parcel of land has become exhausted because of overgrazing or other natural/unnatural conditions. At this point it may be necessary to make an educated guess about how to proceed.
An exhausted pasture will only make your livestock work harder to eat poorly. There are two basic ways to go about renovating that are better than many other ideas that I have read about.
The complete re-do. This would be if you have the luxury of time and can afford to beg borrow or rent a tractor, tiller, and seed. I would warn that this approach should only be used if the pasture if so compacted that nothing will grow.
Even then, it is hard to get a nice bed of soil to lay down from disked up hard ground. It can be done though. Benefits of the starting from scratch method of pasture renovation are complete control over seed mix and this style of renovation is especially nice if you are removing fences or a lane or building and would like to incorporate that area with an existing pasture. The result should be near uniform crops if done well.
The other option is far more likely, as there is no destruction (per se) just modification. If your pasture is over run with weeds but has a healthy stand of clover or grass then you might try a less drastic approach.
Certainly a good way to start is to decide if your critters need to be taken off of the land. If your favorite grazing crops are nibbled down, then the answer is yes.
If the critters have left healthy stands of weeds in the same area as the favorite crops, then it is time to mow. Mowing will abuse the weeds while hopefully not damaging the others.
If the weed problem is small enough, go ahead with your sharp shovel and just cut them down that way. Save the pasture the abuse of driving over it.
A third and compromise approach between the complete renovation and managing renovation would be to break the pasture into sections and try both approaches. This might work well if part of the pasture is worse off such as the area around the water supply or where you give the animals attention.
Keep in mind that the area for complete renovation will need to void of critters for several months until the seedlings sprout and have a chance to take hold.