Asphalt driveways are more commonly known as blacktop driveways. Due to the weather conditions, thickness of your asphalt, the base under the driveway, the quality of asphalt used along with many other factors are the reasons for splits in your blacktop driveway.
Blacktop is a soft material which makes filling splits easier, but because it is a softer material it will split easier. There really isn't much you can do to prevent splits from forming, but they do need to be fixed as soon as possible. If the blacktop splits are not fixed quickly, rain, snow, and ice can get into the splits and cause the driveway splits to widen, deepen and possibly lift the driveway.
Always fill splits when the outside temperature is over 60° because the split repair material will be easier to work with and in colder weather the material will not adhere to the existing blacktop and it will not set up.
Clean the cracks. Use a stiff brush, shop vac or powerful leaf blower to remove dirt, debris, leaves and weeds from the cracks.
Buy asphalt crack filler which is available at home improvement stores and hardware stores.
OR Make your own blacktop crack filler. To mix your own blacktop crack filler and save a little money:
Pour liquid blacktop or liquid driveway sealer into a small clean bucket or a clean paint can or coffee can. Use a container that you don't mind throwing away because it will be thrown away.
Fill the container a little less than 1/2 way.
Slowly add clean sand.
Stir continuously with a strong piece of metal such as rebar. Rebar is used to reinforce cement and can be purchased at home improvement stores and hardware stores.
Continue to mix and add sand until it has the consistency of putty.
Use a trowel or metal spackle knife to fill in cracks.
Pack the mixture into the crack as far as possible.
Add another layer of the sealer and sand mixture so that it is about 1/4 to 1/2 of an inch higher than the rest of the driveway surface.
Use an old piece of wood and a mallet. Place the wood over the newly laid filler, bang the wood with the mallet to tamp the crack filler down until it is flush with the rest of the driveway surface.
Allow the asphalt crack filler to set up for a few days.
Apply 2 coats of liquid blacktop sealer to protect the surface.