Here is the easy way to prepare it at home. If you have no time, there is always an instant dashi powder for you. So don't feel this a burden!!
Put 600cc water in a pot with 5 square-centimeter of dried kelp. Leave for 10min. Put to low heat and remove the kelp just before the boiling point. Bring the water to a full boil. Add a little bit of cold water and put a handful of bonito flakes(about 5g). Turn off the fire as soon as it came to boil. Leave for 30sec. Filter it to remove the bonito flakes from clear dashi.
Besides making dashi with bonito flakes and kelp, there are varieties of dashi. Kelp dashi or shiitake mushroom dashi is used for Buddhist cuisine which is vegetarian. Sardine dashi is used when you want more strong and fishy flavor. And so on...