On Windows, you can open Character Map, find the character you want, click, copy, and paste.

For characters you enter frequently, if your keyboard has a numeric pad, then you can use the Alt key and a numeric code as described here:

https://support.microsoft.com/en-us/topic/insert-ascii-or-un...

Unfortunately that doesn't work with the number row, only the numeric keypad.

On any OS, you can find several similar character tables online:

https://www.google.com/search?q=unicode+character+map

In addition to the Character Map and other tips, you could also try just pressing the circumflex character[1] and then 'e' (or some other letter). Works for me without running any special utilities like mentioned in a sibling comment, but Idunno if that's down to something similar built into the non-English keyboard driver or something. You can but try.

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[1]: On my Nordic keyboard it's somewhere to the right of P or L, but on an English one it should be Shift-6 (or AltGr-6?) in the top row, according to https://en.wikipedia.org/wiki/Keyboard_layout

On Windows, there's a program Win Compose[1], letting you press Compose e ^ to get ê. On Linux (Xorg/xcompose), that's built in but you may need to map a key to Compose. I use right control.

[1]https://github.com/samhocevar/wincompose

If you are on a windows machine with a numpad, hold alt+ 0234 for lowercase or 0202 for capital. Within the Microsoft office suite you can press ctrl +shift+6, release press e. And there are similar shortcuts. You could also use the character map program included with windows to copy it to the clipboard.

On macOS you can either hold the e or option I + e. Iirc