Those familiar with LaTeX may find the following tool useful: http://www.unicodeit.net/ It takes LaTeX symbols as input and outputs the unicode for them. There is a mac app available too, which will convert it in-place for you too.
Then I copy the character into the document I'm working on. Others have more efficient ways to enter Unicode from their keyboards, like having a list of codes and a keyboard layout that allows the codes to be entered efficiently.
also, most platforms I have used have some kind of software to look up characters, e.g. on OSX you have something like "character map" where you can search by name/category