How to tell which colorscheme a Vim session currently uses

There's no guaranteed way (as a colour scheme is essentially a load of vim commands that are sourced). However, by convention there should be a variable g:colors_name that is set to the name of the colour scheme.

Therefore, try this:

echo g:colors_name

If you get E121, it's either a poorly made colour scheme or it's the default one.

A shinier way of doing this is (for recent versions of vim):

function! ShowColourSchemeName()
    try
        echo g:colors_name
    catch /^Vim:E121/
        echo "default"
    endtry
endfunction

Then do:

:call ShowColourSchemeName()

If it says "default", do :colorscheme default and see if the colours change. If they do, you're using a malformed colour scheme and there's not a lot you can do about it other than manually switching themes until you recognise it.

The variable g:colors_name is documented here:

:help colorscheme

Best option is to use :colo or :colorscheme in current vim and the actual colorscheme text is shown. Please see,

:help colorscheme 

for more details.

A one-line version of DrAl's answer:

let current_scheme = get(g:, 'colors_name', 'default')

The get() function will fall back to 'default' if the variable has not yet been set.