Can I change my own transmission fluid on this car it has no pan or drain plug.

Hello, If you are unable to find the drain plug, it is best to leave it to a professional technician. Not to be rude, or sound patronizing, but it really is a risk to your vehicle if you are not confident in the repair. The transmission can be serviced, even "sealed-for-life" transmissions can be serviced, but knowing the procedure for particular transmissions is a necessity. Let me know if you have questions while servicing your vehicle, otherwise, I'll leave a link to certified shops in your area. http://repairpal.com/buick-within-10-miles-of-mansfield-missouri-65704