>I plowed my fields and then it rained for the next four days. By the time
>the fields dried and there was time to get back in and disk, the fields were
>full of weeds. What is the best way to handle this situation? 

Disk or tillage tool (spring tooth harrow/cultivator) them under, stems and all, and let them rot, completely covered by dirt.
If you have a tractor-mounted rotavator then till them under completely with that. Harrow (disk or toothed) them before or after rototilling only if necessary.
If they are not tall then the tototiller will remove them and often if they are tall as well. If tall then try disking to cut them up then rototill.
Problem exists when the weeds are tall and tough stemmed, like lambs quarters, goldenrod, ragweed, redroot pigweed sometimes, Pennsylvania smartweed
and Johnson grass. Then the only option is to rototill multiple passes, or bottom plow, or disk harrow, whichever works with the soil you have and the toughness and height 
of the weed stems. Often there is a problem using plow, lightweight disk harrow or toothed harrow when the weeds get pulled out and bunch up with soil in front of the tillage tool.
If this presents an insurmountable problem then bush hog the field first. Best bet is to till under any weeds as soon as they emerge or before they are 12" tall.


tillage tool/spring tooth harrow/field cultivator

3 bottom, trip bottom, moldboard plough -1
3 bottom, trip bottom, moldboard plough -2
3 bottom, trip bottom, moldboard plough -3

60' 3-point-hitch Howard Rotavator

bush hog mower

Yeomans plow, for deep tillage/subsoiling, to leave soil surface undisturbed and not inverted, useful in notill applications -1
Yeomans plow, for deep tillage/subsoiling, to leave soil surface undisturbed and not inverted, useful in notill applications -2
Yeomans plow, for deep tillage/subsoiling, to leave soil surface undisturbed and not inverted, useful in notill applications -3
chisel plow tines mounted between hilling-bedding disc implement; useful for cultivating, weeding and making and maintaining large 
raised beds for market production

hiller-bedder with chisel plow tines (all 4 currently mounted side-by-side, in one row on front toolbar (leaves beds wider and taller)

hiller-bedder with chisel plow tines -1
hiller-bedder with chisel plow tines -2

hiller-bedder before chisel tines were added

hiller-bedder in use in the field making long raised beds -1
hiller-bedder in use in the field making long raised beds -2

beds with crops -1
beds with crops -2
beds with crops -3
beds with crops -4
beds with crops -5
beds with crops -6
beds with crops -7
beds with crops -8
beds with crops -9

beds after formation, before planting -1
beds after formation, before planting -2
Beds mostly weed-free from using the methods described above: 
tillage, timed just right and with the right implements; cover-cropping, intercropping and allelopathy helped also.