This is common myth, and pretty easily debunked. Try singing normally. Now sing exactly the same way but open your mouth wider. Does your voice get better or louder when you open your mouth? Of course not. It might get a little clearer, but that's probably it.
Here's a better tip: open the back of your mouth slightly wider when you sing. You may have noticed that singers often add "reverb" to their voice when recording a song. You may also notice that you sing better in the bathroom, or that your voice is louder in a cave. Simply put: sound tends to be prettier when it flows freely, and it tends to be louder when it has an enclosed space to bounce around in. Producing that bathroom/cave effect in your mouth by opening up the back of your mouth will help to achieve these results. (Opening the back of your mouth lifts your soft palette, lowers the larynx, and opens the throat. Like everything with singing, don't overdo it. Don't open up further than feels comfortable.)
This is another myth that you hear a lot. If you do some searches on the internet you'll find this one debunked quite a lot. To make it simple: you already support your voice adequately when you talk. If we didn't, we wouldn't be able to speak. Singing is sustained speech and thus uses more air, but that's it. Rather than frustrate yourself with useless efforts to squeeze and strain and contort your breathing apparatus in various abnormal and ineffective ways, focus instead on doing a good job of filling up your lungs, and then regulating that airflow with your abdominal muscles. Singing or talking occurs when air passes through our vocal cords. Think of a balloon. Many teachers talk about the idea of filling a balloon. But can you let air out of the balloon and replenish that air at the same time? Not really. Some teachers talk about keeping your tummy rock hard. In the context of a balloon, that's like continuing to blow air into the balloon and never stopping. That's not really possible, right? Eventually you have to stop and take a breath. But more than that, as long as you are blowing into the balloon, no air can come out (assuming it doesn't have a puncture in it). In the context of singing, if no air is coming through your vocal cords, there is also no sound. So this idea of keeping your tummy rock hard while singing is rather silly. The very idea of a rock hard tummy suggests pushing your tummy out. Try that with your balloon. Can you regulate the airflow from the balloon by pushing out? Of course not. Same with the rock hard tummy idea. It makes no logical sense. Instead, blow up your balloon full of air, and then slowly let it out a little at a time, squeezing your fingers to regulate the airflow.
To recreate this in singing, take a breath in to fill your lungs, and then slowly let it out, using your abdominal muscles to regulate the airflow. Use those muscles to keep a slight squeeze at the top of your "balloon".
A Few GOOD Singing Tips:
Keep your tongue forward. There's a tendency for the tongue to sneak back into the throat when singing. As you can imagine, it just gets in the way. Try singing normally, then try putting your tongue further forward, say in front of your teeth, and sing again. You probably won't be able to enunciate very well with your tongue like that, but your throat should be clearer and you should produce a better, clearer, easier sound. Pay attention to your tongue when you're practicing and just make sure it isn't sneaking back into your throat. Some teachers suggest keeping it forward and flat, others suggest keeping it pressed against your bottom teeth so that it is curled up in the middle. Experiment a little and see what works best for you.
Open the back of your mouth. It shouldn't be as open as a yawn, but just a little more than normal. Again, experiment and see what works best for you. It should never feel strained or strangled or uncomfortable in any way.
Fill your lungs. Practicing by breathing in with a slight "tss" or "kuh" sound can help you get more air.
Use your abdominal muscles to let your balloon (your tummy) deflate in a slow, steady manner.
Experiment with lots of weird sounds. You'd be amazed how helpful weird sounds can be in developing your voice. A few sounds to get you going include nasal, baby crying, and sirens.
Learn to sing on a "shortened" vocal cord. Think of your vocal cords like a zipper that zips towards the back of your throat. The more you zip it up, the higher you can sing. It may not sound like your normal speaking voice, but that's fine. When you properly utilize a shortened or "zipped up" vocal cord, you can bridge into different registers. The lowest register is typically called your chest voice. That's the one you use every day when you're talking. Chest voice is your thickest, fullest register. The next highest register is called head voice. It is very similar to falsetto, and in men it is often mistaken for falsetto. For most of your middle notes, you should use some blend of chest voice and head voice. Many men can't access their highest notes because they sing too high using only their chest voice. Then they hit their head voice and their voice "breaks". This break occurs because head voice and chest voice sound very, very different if you compare them separately. With practice, you can learn to blend head voice with chest voice, thus eliminating your break. Remember to use more and more head voice as you get higher and higher. Head voice is a thinner, lighter sound. If you're straining or yelling to reach high notes, you're probably not using enough head voice (chances are you're stuck totally in chest voice). With practice and training, men can hit even high soprano notes, though the need to do so is very rare. A great example of good vocal technique, including blended or "mixed" voice, and the many different registers you can hit, is a guy named Nick Pitera. Look him up on Youtube, he's pretty amazing. If you really want to get crazy, spend a little more time on Youtube and look up some videos of people using "whistle register". It's the highest of all registers, and there's really no reason to use it other than showing off, but it's pretty interesting.
Eliminate all tension in your face and neck. Your face and neck should be very relaxed when singing. Their only job is to shape the air as it passes through. All of the heavy lifting is done by your abdominal muscles. If you have tension in your face or neck, your voice will likely sound tight and strained. It won't flow freely and "ring" with that clear, bell-like quality that singers strive so hard for.
HAVE FUN! Ultimately, this is why most people sing. Please, don't let anybody destroy your love for singing. With practice and the right guidance, anybody can be a decent singer. That includes you. Remember though: you are the only thing you can control. Some people will love your singing, some people will hate it. This is true even for the professionals. Some people love opera singers, some people don't. Some people love country singers, some people don't. Ultimately, you can't control what people think of your singing, so don't even try. Just keep practicing, sing the kind of stuff you enjoy singing, and have fun.