Since you are entering Thailand overland you will be stamped in for 15 days as you have a U.S. passport, and there will not be any fee. This is commonly called a "Visa Exemption". You may be required to show proof of onward travel within 15 days.

You do not need top do anything special, other than present your passport and possibly show proof of onward travel, when entering northern Thailand from Laos.

At Suvarnabhumi Bangkok International Airport (BKK) you will remain in the international transit area during your connection to VTE. You will not pass through Thai Immigration.