Just lower the master volume until the volume doesn't hit the red anymore (0.00 or negative)?
That's the fastest way. Just lower it. I would follow the guidelines mentioned, start the mix at lower levels and leave headroom. Gauge your loudest potential hit in the loudest section, ie. kick/snare, and go from there.
These days I'm WAY below 0dbfs, I mix nearly with nearly 20db of headroom.
Inherent things that can make a tune difficult to make 'competitively loud' without clipping or sounding small, are (casually and opinion):
Sympathetic arrangement - every part plays a distinct musical role (kick is one role, bass is another, they do not compete)
Distortion/harmonics - harmonics make sounds perceptually louder by masking the fundamentals (lowest/highest power bass frequencies). Mask is a bad word, but in essence less fundamental, more harmonic, because we are sensitive to higher frequencies. Harmonics by definition are related to the fundamentals by octave, so it is worth some understanding to take advantage of. For sounds that are very powerful (kick, bass, toms) that need to be heard without taking up headroom, you can mix these in much easier without swallowing the tune with too much low end power/headroom
Compression in stages - A little peak reduction at every stage, using appropriate attack and release times is a lot more forgiving than attempting to reduce a peak in one go. Use busses that go into busses, where each stage supports the last. These busses allow you to control signal level from the micro elements to the macro/group elements. This takes practice and organization but it pays off. Especially later when you need to make level corrections. Remember the duty of each compressor in each stage so you can make deliberate adjustments.
Low Shelves - gentler than HPF, these can be pulled down for a much more transparent/subtle power attenuation. You have the slope, frequency and level to balance, it's a softer curve and has less impact on the whole signal, than pass filters. Shelves are a ton easier to go into later and make a tiny adjustment, rather than brutally dragging a 24db up 10hz. With these gentle adjustments, you will be less likely to fool yourself into adding 'bass' because you had your filters pulled in too far.
Get rid of extraneous BS - overlapping drums, bass hitting under a kick, too much happening at breaks, a synth that plays no role other than just being cool, competing frequency ranges, notes that are out of tune, tail on the kick, low end on that snare. If you're making your own tunes, your in your own head. Get out of it and don't fall in love with everything you did. Ask yourself is it really necessary in order to express my idea?
Listening levels - Does the tune hold up when listening at low level with say the AC on? If your bass/kick disappear, if your low level background pad drops off, consider the distortion/harmonic thing rather than the volume fader. Low level monitoring is all about perception of loudness. It may be that the low end and kick are too loud at low level. Check to see if this is caused by fundamentals, or by harmonic distortion. This is very important in assessing potential loudness capability. Fundamentals eat headroom, we should not hear them at low levels. Look up Fletcher Munson.
Mono monitoring - listen to the difference in perceived power between a signal that is duplicated in both monitors, vs 2 similar signals playing back simultaneously. Mono signals are more directional, they register as more forward than stereo signals. When you reference mono you are making everything equal. Anything that wasn't equal (stereo) will be summed and cancelled. Be aware of the difference and make assessments on instrument priority here. If you need it up front and direct, make sure it remains so in mono. If it's to be placed behind, make sure it's not competing in mono. Even if all percussion is mono, they still need be placed for separation. Mono listening (with one speaker) forces you to balance based on actual power coming from cone. Stereo involves listening to a phantom image (area in between the monitors) of instruments that are mono or mono-like. Your brain does the summing, you listening position determines the quality. I can mix drums so much faster in mono, no second guessing, and when done and checking in mono, they are more spacious, wide and deeper than I could ever do with a phantom representation.
Come back later - Finish a tune and let it sit for a week or two, work on something else, separate yourself from that song. You may find that it becomes fresher, things may annoy you that you didn't hear, ugly distortions may be more apparent, the odd loud HH will stick out, the bass may be too loud, all percussion probably needs to go down 2db, you can get rid of more BS and prioritize the elements that you remember were the focus of your expression.
Practice - practice this stuff, gauge your results and apply your findings to the next project. You may find that you're avoiding the previous pitfalls from the start. You might start off my making busses, just because you already know that you needed to compress drums as a group on that last project. You might select some instruments that are mono this time, you may take time to make serious considerations to sound selection and arrangement, maybe you have this time decided that you don't need a bass to sustain under the kicks, maybe this time from experience, that kick did not need 50hz. Last time you may have been trying to EQ and EQ that kick, cutting this and that away from the bass, sidechaining random elements, fighting this and that. Prep your working area in a way that lends you to make deliberate adjustments that do not ruin the balance of your hard work, set yourself up in a way that separates low end from mind range from high end, keeping those processors separate, so adjustments can be fine tuned for perceptual balance...bass too low? OK, work on midrange. Maybe -.05db on that low shelf. Maybe bump up the distortion send. Remember the roles. Be able to control them specifically on micro and macro level.
