A rubber bulb syringe can fairly easily clean out earwax at home. In some cases, the earwax may need softening prior to using the syringe.
If earwax is hardened, it is best to first use a dropper to insert a few drops of coconut oil, baby oil or hydrogen peroxide into the ear canal. If peroxide is used, take the syringe and fill it with warm water. Gently squirt it into the ear canal, pulling the outer ear back to straighten it. Then, let the water drain out of the ear. Repeat, if necessary.
If any oils are used to soften and loosen the wax, use the syringe to expel it. It is important to remember to dry the ear after this process with a towel or blow dryer, as excess water can occasionally cause problems.