Set up a temporary garden or party tent over the driveway if the rain is pouring down or is not forecast to diminish for several hours. Tents with side flaps work well, particularly if the wind sends rain gusts over the driveway.
Clean off any debris from the area where you want to make the repairs; an area free of dust, dirt or grass clippings allows the repair to bond better. A stiff bristle broom, garden hose or leaf blower works well for this task.
Read the instructions on the asphalt emulsion compound, often called liquid asphalt. Some compounds require diluting with water and using a spray bottle while others may be brushed on the area. Add the correct ratio of water into a spray bottle -- if necessary -- and then spray or brush it on the area under repair. A paintbrush is a handy tool for this task.
Warm the bag of cold-process asphalt mix by placing the unopened bag in a bucket of hot water. During sunny weather, placing it in a spot where it receives the sun's warming rays works well.
Use a putty knife or an asphalt crack filler to fill the large crack or hole with the asphalt mixture. Allow mixture to mound slightly in the area and then tamp it down. Use a metal tamper or a piece of lumber to tamp it even with the surrounding asphalt.
Soak up any standing rain water in the depressed areas with paper towels or an old towel. The depression can be slightly damp from the rain as long as no water is puddled in the area.
Apply the asphalt emulsion compound to the depression according to the directions on the label.
Spread the cold-process asphalt with a trowel so the depressed area is even with the surrounding asphalt.
Tamp down the cold-process asphalt with the metal tamper or a piece of lumber. Add more asphalt if necessary.
Wait 24 hours for the cold-patching material to dry adequately before using the repaired section of the driveway.