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To visit the UK you will need a Standard Visitor Visa. You can see on its page that you can apply online.
When you apply online you need to:
You can save your application form and finish it later. For the US an application center would be at a US DHS application support center (ASC)
For a Schengen visa, you will have to download the application form and submit it along with all relevant documentation to the embassy or consulate of the country you will be entering first or residing the most days in the trip. The list of documentation would be something like
You should check with the embassy if any additional documentation is required or not.