It is super important to train our core. Why? Because all of your basis of fitness comes from the core. Think about the definition of core which is this: a central and often foundation part usually distinct from the enveloping part by a difference in nature.
How do you strengthen your core?
1. Abdominal crunches at all kinds of angle. One of the most basic core exercises is hold your stomach tight. You can do this while sitting at your desk, driving your car, etc. Challenge yourself to hold it.
2. Plank type exercsies. When doing a plank be sure to hold your stomach tight, pull it away from the floor.
3. Lower back exercises. Did you know your lower back is considered core? If you only strengthen the front of your core your lower back will suffer a muscle imbalance. Do so by doing superman holds, lower back machine use, and/or use the back extension.
I recommend working the core at all different angles, remember your obliques. And your lower abs work differently that upper abs. Feel those muscles as you work and you will find how to strengthen your core.