The most important area for parents to concentrate on are literacy skills. Children should arrive at kindergarten knowing their letters, how to write their name and how to read some basic words. This may seem like a tall order for a busy parent, but having these skills before school begins is necessary. In kindergarten, you can expect that your child will already be bringing home books to read and taking spelling tests and your child will need to be able to keep up.
Math skills are also important for your child but are often easier for him to learn at home as he has to count basic items on a daily basis. Your child should be able to count items up to 20, and he will need to understand the principle of adding and subtracting, even if he can't do an addition or subtraction problem on paper yet. He should also be able to recognize numbers under 20 by sight and write them. Shapes and spatial relations are basic skills that he will be expected to know as well.
Science is often considered more of an upper-level subject, so it isn't as pressing for young children to learn right away. However, your child will need to have a basic understanding of nature and cause and effect. She should also know how to find out information about nature or what she observes in her environment; so don't just tell her factual information, help her explore and learn on her own. This self-guided discovery will help her in all subject areas later on.
Aside from the three big areas of concentration in academics, your preschooler will need some social skills, too. All children will need to be able to listen in class, control their impulses, take turns and socialize with other children and adults. Additionally, you should introduce your children to the concept of empathy, which means treating others according to how they would like to be treated. These skills come easily for many children but are a challenge for others. A parent can foster these skills by organizing play dates for their child or taking them to events with other children.