Depends on the situation. In a yard or garden, smothering is less work and quite doable. In a pasture or crop field (and, when you do own a tractor), it is often more feasible to repeatedly cultivate a large weed patch.
But, you say "burrs" -- do you mean burdock? Unless it is a large fairly pure stand (in which case, repeated cultivation during the year would work, if you feel like it and don't mind sacrificing then reseeding the area), your best bet is really to dig up the plants by hand. It works best that way.
The 3-step burdock cure:
1) remove all standing dead plants (because you don't want them reseeding!) to a burn pile or at least far away in a fallow field. Do not worry about digging -- once a burdock plant has flowered and set seed (burrs), it dies on its own anyhow, they are biennials.
2) Once the plants start growing in spring (and not too long thereafter, i.e. it is better not to wait very long) go out there with a shovel. Dig up each plant you can find -- it will just be a flat rosette of increasingly-large leaves. you needn't necessarily get the WHOLE root, but get as much as you can. It helps if you use a mill file to sharpen your shovel before you start in on this. You needn't do anything with the dug-up roots, just leave them "toes to the sky" on the ground to dry out and die.
3) Then in late summer, walk the pasture again to look for survivors trying to flower. WAIT TIL THE FLOWERS ARE OVER, AND THE BURRS ARE STARTING TO SET (but still green and flexible), then lop the stalk off at ground level (dispose of as described above) or dig up with shovel and dispose of. If you do this too early, like when the plant is still flowering, it will just throw up a new flowerstalk, closer to the ground and much much harder for you to find. (But not harder for the horses' manes to find, and it reseeds just fine!)
After a couple years of this, you can have a truly burdock-free pasture.
Good luck, have fun,
Pat