The larger the voice the more time is needed to warm it up. However, the quickest, best way is to first warm up the chest register. Sing one note, straight tone, in a comfortable forte in the lower-middle portion of the register on a single vowel. I like to start with "eh" or "ah". Simple, non-fast movement is the best way to get blood flowing to the cords. I also do a 3-note descending pattern (E-D-C) on a vowel, slowly. I work as low as I can go first, then go higher as is comfortable, but not my highest in chest. Then I warm up falsetto by singing on "oo" or "ee", again, just one note, straight tone, in a comfortable forte. Then I also do the descending pattern in the falsetto range and go as low as I can in that register without breaking into chest.
Then back to chest for an ascending pattern (C-D-E) singing "eh-eh-oh" starting out low in chest register and going as high as comfortable. After that, I will do some octave yodels singing in chest on "ah" or "ee" and then yodeling up into falsetto/head voice on "oo". I make sure that before I yodel that the bottom note is straight and secure, and when I go up into falsetto I may add vibrato then. After this I'm ready to work the falsetto/head voice higher.
I can do this in roughly 10 minutes, and I've had to warm-up in the car before many an audition or performance. Not ideal, so I usually will have sung a bit before I leave or earlier in the day if possible so that the warming up process is faster.
note: I use falsetto/head voice because I am a woman and women do not really sing in pure falsetto, so anything we do is head voice which is a falsetto-dominant sound with some chest participation. Men, however, can sing in pure falsetto and so should work on singing in that without any chest participation.