The short answer is, don’t.
The long answer is, do not overstay your visa.
In the past, I have heard of many people who have overstayed their visa and simply paid a fine upon leaving the country. At the old airport there was even a room designated specifically for visitors who overstayed their visa. Without wishing to sound too dramatic, much has changed in Thailand in the past year.
It’s up to you whether you overstay or not. The best-case scenario now is a fine of 500 Baht for each day of your overstay. The worst-case scenario is detention in a Thai prison and deportation. The latter has happened to people who have overstayed by a few days and were en-route to renew their visas. The choice is yours.