It's actually not especially difficult to fill asphalt yourself as long as the job is simple. The important thing is telling the difference between jobs that are simple and those where you absolutely have to have a professional's help.
If the area that you are seeking to repair looks like the skin of an alligator, with interlacing cracks that look like the reptile, this is not going to be something you can handle yourself. Part of the reason for this is because it has multiple causes that can change the best means of treating it.
Many of these causes are also going to be beyond the ability of a layman, such as poor drainage underneath the base of the asphalt. Filling it would be pointless since it would just immediately crack again.
In the end, this means that if you notice one of these patterns, you really need to go find a professional. You could make the problem worse if you don't get the help of someone with training in asphalt repair.
Straight or Zigzagging
If the crack is a single line, then you can just buy asphalt crack filler in order to solve the problem. It should largely be a single line, though, even if it moves diagonally back and forth. You're in trouble when you have multiple lines all connected together. But, a single line you can just fill up once you buy the supplies you need.
It's actually important to fill up these as quickly as possible since otherwise they will fill up with vegetation. Plants will grow in the areas and make matters much worse with expanding root systems. The crisscrossing pattern could even go beyond the realm of easy repair if you wait too long to get it done.
You can use a trowel to fill cracks that are 1 to 2 inches wide, and this is doable by yourself. Deeper cracks you will want to fill in with gravel in order to get them within 4 inches of the surface before using traditional crack filler. This is often a situation where calling a professional who use the filler for you is a good idea, just to make sure it is done right.
Overall, you want to take a careful hand whenever you try doing any of this completely by yourself. It's worth being ready to call in the professionals at any moment if you feel overwhelmed. For more information, contact a company like Gopher State Sealcoat.