The basics of soil compaction management are in order of importance: (1) help your soil resist and bounce back from compaction; (2) avoid causing compaction; (3) remediate compaction only if needed.
You can make soil resist compaction by practicing no-tillage for the long haul. No-till soil has a unique architecture with firm aggregates interspersed with macropores. The firm aggregates help support weight from agricultural machinery or animal hoofs, resulting in significant reduction in likelihood to create ruts in the field.
No-tillage also stimulates organic matter accumulation at the soil surface which helps reduce the effects of surface compaction because soil with high organic matter content is 'spongy' and less compactable.
The permanent burrows of old root channels and prolific activity of earthworms and fungi in permanent no-till soil also helps make the soil resist compaction, while the biological organisms also help alleviate compaction after it has been caused.
Living root systems are probably the best protection against compaction. Just choose where you'd like to walk on a soggy day; on grass sod or bare soil? Therefore, it is recommended to plant cover crops right after harvest of annual crops to keep living roots in the soil year-round.
The living roots also help soil bounce back from compaction. The living roots produce exudates and are often 'infected' by mycorrhizae that have fine fungal hairs and produce their own exudates that stimulate aggregation in the soil.
To avoid compaction is a lot more cost-effective than causing it and then having to repair it. So farmers should do whatever they can to avoid causing compaction. Avoid driving on wet soil is number one. Keep the cattle out of the field when the soil is wet. If the topsoil is frozen or if the soil is very dry little compaction is caused.
But in farming we often have to get into the field when conditions are sub-optimal. Some other things that can help are to use flotation tires or tracks that enable you to 'float' over the soil.
It is important to use the minimum allowable tire pressure in your flotation tires or you won't have the large footprint that helps reduce the sinkage and high contact pressure that cause surface compaction.
Using low-inflation tires on tractors also helps to reduce slippage and increases horsepower output of your tractor. Further, the axle load is important, too. It is recommended to keep axle load below 10 tons - to help avoid causing subsoil compaction.
Finally, what if, despite all your best efforts, you still have ruts in the field?
Before doing any tillage you have to remember its negative effects. Therefore it makes sense to limit tillage as much as possible and only use it sparingly. If ruts are limited to depressions in the field, it may be possible to use a backhoe, or chisel plow or disk mounted on the three-point hitch to smoothen the ruts.
On the other hand, if ruts are distributed across the field, it is probably necessary to smooth out the whole field. If the soil in the bottom of the ruts is severely compacted it may be necessary to do deep tillage to remediate that.
New subsoilers don't do a lot of surface disturbance which keeps residue cover in place. This is important because the mulch helps reduce drought stress in the summer.
The best time to do subsoiling is when the soil is dry to cause maximum shattering. Unfortunately it may be difficult to find this condition before corn planting time. Using a field cultivator to smoothen the ruts is recommended above a disk to keep more residue at the soil surface. Tillage destroys soil structure.
So now it's important to help nature to build soil structure back up; primarily by planting your crop or cover crop soon after the tillage is done. Building organic matter content with manure or compost applications is also helpful to restore your soils to productivity.