So I've seen a few of these kinds of threads here, and I got a good laugh from the majority. That being said, my next thought was 'why not give it a go?' So...
My first assumption would be that the only people to read this will either be beginners, or people looking for a good whinge, and a chance to post a twatty comment. If that's true, then I suppose this is the disclaimer; 'Everyone has their own opinions, and I won't be offended by yours if you aren't offended by mine'. This is MY how to thread, and therefore are MY opinions.
INSPIRATION/GOAL(S): I won't waste your time qualifying myself, and I won't waste my time name dropping. The best thing I can say for beginners is to determine what you want to express in your song(s), and research artists similar to this vision, i.e.; thrash, hardcore, reggae-fusion, horror punk, political punk, anti-folk, whatever. If you can't find something that tickles your fancy, then just listen to your favorite bands.
CREATIVE EXERCISE: I in no way condone plagiarism, I simply ask that you find a muse. Find a topic, and a sound that you admire, and find a way to achieve a resemblance in the sound. For example, the Ramones' songs early on (for the most part) consisted of power chords, fast strumming, little to no palm mutes, bass lines that mimicked the guitar to a tee, and a simple beat. Whereas the Clash would throw in barre chords, lead guitar, more complex bass notes, high treble on bass and guitar, etc. Find what makes these sounds so different from each other, and your on your way to becoming a theorist.
When I first started writing songs I did this as an exercise. It wasn't a formula for writing songs. I found riffs, chords, rhythms, bass lines, melodies, a whole ton of things from all different sorts of bands (some not even punk) that I could incorporate into my songs that would spice them up when I felt they were going flat.
EXAMPLE: One of my first punk songs was a satire on the genre (Pete the punk'). It was simple enough; verse, chorus, verse. But it didn't sound interesting enough to me. Until I came across a chord I had never seen before in a Frank Zappa song; a D#9dim boy did that f--ker sound AWESOME to me! I had to find a way to put it in my song. I strummed my open E chord twelve times in rhythm with the song, then played the weird ass note, and before I knew it I had an intro for my song. This is just an example, but by the time I was done tweaking my otherwise mediocre song, I had written something actually worth listening to. When the band I was in would play Pete the punk', the audiences' heads would bob their heads up and down with the D#9dim like they knew it, and were friends with it.
(In digression) To those too impatient to do this, I suppose it would just be easier to generalize, and tell you a few tips to achieve certain sounds in punk guitar. I won't bother with the argument of formula vs. creativity', as I assume that you are either too lazy to care, or just a beginner. It's pointless to say that all punk guitar sounds the same, as this is obviously far from the truth. Instead I will categorize, and classify. There is;
GENERAL PUNK SOUND: (Sex Pistols, the Clash, Stiff Little Fingers, the Germs, the Heartbreakers, Dead Boys, the Rezillos, etc.)
These bands primarily had a more treble based sound to their guitars, and a scooped-out' growl to their basses. Part of this had to do with the pick-up's of the time. But if you wish to achieve this sound, I suggest you switch to the pick-up farthest from the fretboard, and turn tone all the way up. If this is too twangy for your taste, then find a middle ground. As for your amp, turn the bass down to about 4 to 6, your mids to about 7, and your treble somewhere around 9 to all the way the f--k up. Surprisingly, you won't need as much distortion as you might think with this, it sounds pretty gnarly already. However, depending on your gear, you might get a different sound, so I must say that these settings are more guidelines than requirements.
90's PUNK, AND ON: These guys have a bit more beef to their sound most the time, so whereas the general punk sound would be more focused on treble, you may want to focus on a mids, or mids/treble mix. Set your guitar to the middle pick-up, and put your tone somewhere in the middle to a quarter to the max. Your amp can either have the bass up around 7, or the treble around 7. Whichever you choose, make sure the latter is turned to about 4 to 6. And for fun, turn your mids all the way up. With this sound you can add a ton of distortion too, so that's always good.
This should cover you in terms of punk guitar sound for a while, until you find something better, i.e.; a pedal you like, or some rad ass you've been saving up for.
CHORD PROGRESSION: Some people think there is a certain theory, or method to punk chord progression, whereas others simply say you will need only three chords per song. I disagree with both of these schools of thought again because of the formula vs. creativity' argument. While it's always safe, and easy to keep things in key, I must say that a lot of punk songs don't follow a particular scale. One of my favorite examples at the moment would be the Misfits Teenagers from mars'. While some may argue that this song is in the key of G, I must bring to the occasion G#, C#, Bb/A#, and F that clash with a G major (the songs starting note). This isn't to be a prick, this is just to say that and occasional clash can bring a lot more attitude to a song than any sort of musical purity'.
So how does one chord a punk song? I guess a key factor would be how melodic your vocals are. If you're screaming, or jabbering you won't really have to worry about it; whereas if you're singing, or something close to it, you might have to follow your melody with the guitar roughly. Again, an occasional clash, or III melody between chord and voice could make things interesting. Vague, I know, but I'm sure you can work something out.
LYRICS: This is something of a matter of preference, I believe. Depending on what you're driving for, you may want cheerful lyrics, dark lyrics, egotistical, satirical, perverted, etc. You may be an articulated writer, and you may be a one lining idiot (and this can be appropriate in the right context, at times). It depends on a lot of things. But I would say start from what you know. Emotional energy is one of the driving forces of all music.
You can't write about how ridiculous the economy is if you're parents are paying for everything you can't write about something you haven't experienced without sounding stupid. However, if your parents' financial problems affect their relationship with you negatively, that could be something you could write about. Daddy don't love me cause he can't buy cigarettes and all that. Not I'm workin' nine to five to keep my children alive. These are examples, people. Not lyrics of my own. But you get the idea. Start from what you know, what frustrates you, what makes you laugh, what gives you boners. Or write from someone else's perspective. Also, I find it easier to write lyrics/melodies after writing music, if any of you were wondering. This way I can count syllables to match chord strokes, and rhythms.
IN SUMMATION: Don't take yourselves to seriously on your first go. You may hate your first songs verse and love the chorus, while in contrast you may love your next songs verse and hate its chorus. This has happened to me many times, and when it does I sometimes find that blending the two parts I liked makes a much better song. In short, don't throw away your work. You never know if you have something worth keeping. Keep notebooks upon notebooks of your shit, and go back occasionally for inspiration if you find yourself getting stagnant. Listening to too much of the same music can stunt your growth as well, so when you feel a writers block coming on switch things up. Listen to anything you want. I love the Beatles, but I also love Beethoven, and Nirvana, and even Woody Guthrie. Punk isn't the only thing that can inspire the genre. Danzig was actually a bit of a jazz fan. But I digress!
I hope I have given you a sufficient amount of information, and haven't overloaded you by mistake. All I can really say is take some chances, f--kers. Pick up your guitar and play.