If you find in need of warming shortly before a rehearsal or performance, I would recommend using “humming” exercises in order to simultaneously activate your vocal cords as well as each of your resonance chambers. Any exercise pattern sung with your jaw lowered and mouth closed will cause you to sing at a very low volume, as well as feel a strong vibration sensation in your ‘mask’ area.
Carefully clear your throat for a minute or so, depending on need. Try to expel any phlegm etc. without coughing or harshly clearing. Be conscious of the potential for tiny scratches or irritation on your vocal cords from harsh coughing or loud clearing. Try gentle, constrained exhaling while bent forward, or saying "bub bub bub bub mum mum mum" at medium volume with tightened throat. The goal is to make sure vocal cords and throat are cleared and unimpeded, without abrasion.
Making a soft U sound ("oooooooo") sing your lowest comfortable note, then, while continuing to hum, glide (portamento) up to your highest comfortable note, transversing the falsetto point as seamlessly as possible. Do the same in reverse. Repeat 6 to 20 times, as long as there is no pain or cracking. Do not do anything to injure your vocal cords. This is about gentle limbering.
Starting several notes above your lowest comfortable note, sing varying vowel sounds in five-note ascending and descending major scales at whole or half note intervals. Each time you start a new scale, begin a whole note higher than previously. Start with the first five notes of the major scale, and vary as you like. Stop and reveres, working your way down in a similar fashion, when you approach your highest comfortable note. Use an instrument, pitch pipe, cell or internet pitches for guidance as needed.
With an outward lip roll, sing several major scales up and down, of varying pitch in the middle area of your range.
Repeat step 1 as needed, then sing a verse and chorus of one of your favorite songs, working up to near full volume.
If you're way out of practice, swap numbers 2 and 3. Total exercise time is typically between 5 and 10 minutes. If you can't spend at least that amount of time warming up, it's best not to sing.
Ideally, we'd all have at least 20 minutes to warm up before we do any major singing. Occasionally we are a bit more pressed for time. If you do nothing else, I recommend starting with hums and some of lip or tongue trills. Humming helps loosen up the cords and the lip/tongue trills get you in touch with your breath support, which is essential for singing! Contact me with any need for further clarification here.