Business as usual
During 2020 nothing will change for travel between the UK and Europe for EU, EAA and Swiss citizens. For short visits to the UK, you will not require a visa. You will need a valid passport to enter the UK, and if you have less than six months remaining on your passport please check with the border authorities before you travel. If you are an EU citizen, or from Iceland, Liechtenstein, Norway or Switzerland, you can travel with a passport or an identity card. Identity cards may not be accepted after 2020.
For US visitors to Scotland and the UK, there has been no change and there will be no change to the current close ties of no visa for US and UK citizens crossing the Atlantic for stays of less than 90 days. All you need to do is turn up at the airport with your passport (with at least six months validity remaining) and board the plane as normal. There is absolutely no talk of disruption to flights to the UK and the EU has specifically agreed that there would be no change to any flight rules until 2021 at the earliest.