Full size keyboard numpad method
If you have a numeric keypad to the right of you keyboard, you can type Alt+0163 to get a UK pound sterling symbol on a US-keyboard.
Modern laptop numpad method
Some laptops use a Fn (function) key and overlay the numpad on the main keyboard - so on a Dell Latitude I can hold Alt+Fn and type MJOL (which corresponds to 0163) to get a £ symbol.
...but some modern laptops don't have a numeric keypad at all. For those situations, see below.
Keyboard language switch
Install a UK keyboard alongside the US keyboard in control panel, and then type Win+Space to switch between them. Probably Windows 10 only.
Shift-3 usually types a # (hashtag) when set to US keyboard, and a £ (pound sterling) when set to UK keyboard.
Windows 10 character map (May 2019 update)
Type Win+. (dot) and you'll get a character map with all the symbols you'll ever need! 😊
It even remembers the ones you've used recently for quick access. (❁´◡`❁)
For faster keyboard navigation you can press [Tab] to cycle through the controls and [Enter] to select.
Old Windows method
Open the character map application from the start menu. You can search for it in the latest Windows, or it may be hidden in the Accessories folder for older versions.