If you swallow air when you breath, it can turn into air pockets in your digestive tract later in the day. This leads either to burping or flatulence. There are many different reasons why you swallow air and luckily all of them can be avoided, for the most part, so you can cut down on the amount of gas you experience throughout the day.
Avoid swallowing directly after you yawn. Yawning can bring a large amount of air into the mouth and swallowing afterward is going to send the air down the esophagus. Instead, exhale after you yawn before swallowing.
Breathe with your nose. You are not going to swallow any air when breathing through your nose.
Chew your food with your mouth closed. If you leave your mouth open you are going to end up swallowing a good deal of air with every bite of food.
Wait until your mouth is empty before talking to people during a meal. Talking to people when there is still some food in your mouth is along the same lines as chewing food with your mouth open.
Skip using gum. Gum is going to increase the air flow into your mouth due to your jaw constantly moving up and down, so if you have a problem swallowing air you may want to switch from gum to mints.