There isn't a religion-specific method of teaching young children. Parochial schools likely base their methods off of popular styles -- such as the Reggio Emilia style, with its focus on play, the Montessori style, with its focus on each child's individual growth, and the Waldorf style, with its connection to nature -- then incorporate religious instruction within that framework. Many even blend components of different styles. Work to understand what your child will spend her day doing in the school and think about whether it sounds like something she'll find exciting.
Of course, the religious education is probably the most important reason for you to be looking at parochial schools. Ask about what the school will teach your child about your religion and how they'll do so. Some religious concepts, such as hell, might be too scary for young children, for example, and you might prefer a school that focuses on God's love. You might also ask how the school deals with difficult questions about God or exposing the children to other religions.
Teachers make the school, no matter what type of school you're looking at. In some states, such as California, teachers in private schools are not required to have a current teaching certificate. Though the piece of paper doesn't necessarily guarantee teaching competency, it's often a good start, so ask about the qualifications of the teachers at the school. It might also be important to you that the teachers are members of the same faith.
You'll have to pay tuition to send your child to a parochial kindergarten, and you'll want a good understanding of how much it will cost. Aside from tuition, ask about other costs you might incur, such as providing classroom snacks. Sometimes, a school will give discounts for multiple kids in the family, which can drastically cut costs. The type of uniform might also play a role in your decision. Some schools have a general guideline, such as "khaki pants and navy blue shirts," while others have more strict guidelines, such as a specific plaid. Your kindergartener is growing rapidly and you may need to purchase new clothes halfway through the year. Some schools will offer yearly used uniform sales to help parents with the cost.