There are a few tutorials on how to warm up your voice, so I thought I'd share a few hints and tricks from when I used to do Opera singing.
Don't stretch your voice too far when warming up, there's a tendency to try and go to full range during the warm up, which is somewhat silly since you're just straining your voice more.
Usually if I'm singing for a warm up, I go to about 3-4 notes below/above what is comfortable.
Have warm water handy, honey and lemon drinks do clear the throat well too. Almond milk is very good, but I'm allergic to nuts >_>
For smokers, don't combine milky drinks with the cigarette, try something with fizz but isn't going to become sticky at the back of your throat, then wash down with water.
This works, despite it being weird and it's good for when we forget to warm up *cough*. Purse your lips and force air through (as if you're blowing a raspberry... sort of), it should make a trilling (dppuuuu~) sound. This clears gunk from your throat, if you find you have some :O You can do this at any time, even during a recording as long as you cut it out after...
Humming also helps, it's a way to see how much you've warmed up without stressing your vocal chords as much. They still vibrate and all, but it's easier to keep the tone low and not do damage if you haven't warmed up enough. Just slowly hum higher (or lower), until you hit your limit and see if it's comfortable.
Breathe in through your STOMACH not your chest, you need a lot of air for this next one. Open your mouth and push the air out with your diaphragm, this ought to make it escape sharply. If you want, you can combine this with annunciation exercises by forming your lips into vowel sounds.
Your tongue needs warming up too, as well as your jaw. Some people get aching mouths after singing something like "Ready Steady Go!" >_> Because they warm up their voices but not their mouths. Say a few tongue twisters slowly, and sing a few songs like:
Six thick thistle sticks, standing in a row.
The sixth one is the thickest so that one will be mine.
A lot of the older exercise songs also go up in jumping notes, so it's easier to practice range after your voice is warmed up.
Tips while singing: (These work for non-singing stuff too)
If you notice you're not hitting your high range/high voice, try standing up, making sure your neck is straight and you're not having to look down at the screen to see your lines. Print them out.
Extend vowels if something is lasting a long time. Say someone is shouting: ROOOHHHAAAANNNN~~~ >_> You want to extend the 'O' and the 'A'. Rather than the 'H' and the 'AN' sound. Impure consonant sounds resonate less and tend to warp the word more. (This is why Opera is sang so exaggeratedly, or just in Italian *cough).
If someone interrupts you, finish your line. It can be very bad for your voice to end abruptly, you could strain it. Also ask people not to surprise you or walk in on you... I find sometimes I get bad hiccups because I'm using my diaphragm a lot. -_-
Hopefully that was helpful, I'll try to do some recordings of sample warm up songs.