A visa waiver and a visa are entirely separate things. The former is permission to travel WITHOUT a visa - it isn't in itsself a visa
If you are eligible for a visa waiver then you don't need to go to the Embassy - the green form on the plane is a thing of the past and you must apply online at
A 19 year old UK citizen can get a waiver provided they meet the conditions for a waiver - that is - holding return ticket, staying no longer than 90 days, are not going to work, are not a drug addict or alcoholic, have no real criminal record and a few other things.
some of my family are travelling to the USA later this year and none of them, adults or children had to go to the embassy....all done by application forms
you need to apply for an ESTA which is permission to travel - USA operate a visa waiver system for many european countries- like a visa doesn't guarantee entry -costs £10- five minute form online