Saw or chisel a perimeter around the damaged area. Make certain no cracked or broken asphalt is outside this perimeter. Cut or chisel the perimeter through good asphalt.
Remove the loose chunks of asphalt with a pick and shovel. Break apart and remove the good asphalt inside the perimeter of your cut with the pick. Shovel out any loose or soft dirt and all debris. Shoveling out soft dirt is particularly important for depressions. Soft dirt is why you got a depression in the first place. You want a solid base for your patch.
Fill the area you cleaned with asphalt. Rake it level. Though level, you want the top of the patch 2 to 3 inches above the surrounding asphalt -- crowned. This will account for the compaction of the asphalt when you roll it. If you do not crown the unpacked asphalt, you will get a pot hole after traffic goes over your patch.
Roll the wheel of your vehicle over the patch five or six times to compact it. If the asphalt settles and you no longer have a crown, add more asphalt then repack the patch.