1. The way to have a good idea is to have lots of ideasHave lots of ideas. When you're trying to be creative, there is no such thing as a bad idea. Turn your mental filters off until you're have finished writing and have a demo recording of your song. Realize that most of your favorite bands typically write about 100 songs for a 10 song album; that means 90% of the songs they write and demo are never recorded properly or released. Prince used to write an album-worth of demo material every fortnight. You should apply quality-over-volume when deciding what to release to the public, but volume-over-quality when writing and demoing.
2. Get used to recording demosMake a habit of recording demos. Get used to recording song demos often. I've done this using a four-track app on my phone, traditional four-tracks, and sometimes just Audacity and my laptop's mic. Get used to the method you're using and develop a workflow, so when you are writing and demoing you can do it quickly and easily. Improvise and work with what you have to hand: you don't need new equipment to demo a song.
Get used to demoing vocals. In many ways, vocals are the song: they hold the melody and the lyrics. It is normal to be bashful about recording vocals, and it often feels unnatural and awkward, even when you're at home in your bedroom. But the more you do it, the easier it'll become. Push through it and get the song down, and don't worry about the quality of the take or your singing voice. Record demos even if the song isn't fully finished, or if you're not sure how good an idea is. Realize that who hears your demos is completely within your control. Going back to the mental filters, let your band members, close friends and future-self decide whether a demo is a good or bad.
A further tip: I keep all of my demos. I find it confidence-boosting to see the number of songs I have expand over time, and to track my improvement. There's no good reason to delete them, as MP3s they take up negligible physical or memory space. For me, it helps get old song ideas out of my head so that I can focus on having new ideas for songs.
3. Record lyric ideas as soon as you have themHave a method of recording lyric ideas the instant you have them. Lyric ideas can be a phrase, a sentence, a rhyme, or even just a single word you think sounds cool. Anthony Kiedis from RCHP does this using a small notepad. I do it using a text file on my phone. It's important that you don't wait till you get home because you will forget what the idea was: you have to do it there and then.
The "don't delete" rule applies here too. Your opinion of your own ideas is not constant, it fluctuates over time. What was an awesome song idea yesterday might seem rubbish now, but in the future you'll sit down to write and be desperate but unable to remember your idea. Just keep everything, I often find myself using ideas that are a year or two old by the time they end up in a song. Use the text file for inspiration: it's great for when you're stuck for ideas, when you want to add originality to your songs, and just for writing better songs. It's really helped me with the other points below...
4. Try unusual rhyming schemesMy songwriting has benefited from using unusual rhyming schemes and structures. Internal rhymes (e.g.: helter-skelter) can make your lyrics sound more cohesive and musical. Multisyllabic rhymes can make solo acoustic guitar songs sound more articulate and interesting. Jake Thackray was an expert at this: the song "I Stayed Off Work Today" for example contains a five-syllable long rhyme (miserably broke-military bloke) and numerous internal rhymes.
If you're feeling confident, try deviating from simple rhyme schemes of AABB or ABAB style. If you have most of two verses nearly written, experiment with swappng lines between verses. For example, the first two lines across two verses (say, ABBB ACCC). This is more difficult to write, but it's good for keeping things fresh and hiding a bland or derivative line, instead using it to create a sense of continuity in a song. It's good for disguising obvious rhymes…
5. Try and avoid obvious rhymesObvious rhymes (e.g.: love-above, rock-n-roll-control, fire-desire) are rhymes that appear in countless songs. They can make a song sound dull or tacky. These overused rhymes were the bulk of my songwriting in my first few years of songwriting, and some of my favorite songs contain these obvious rhymes: "Fuel" for example, is my favorite Metallica song.
One alternative is to set the listener up to expect an obvious rhyme, then go somewhere different. A rhyming dictionary (online or paper) provides an alternative that is good if you're a beginner songwriter or find yourself in a rut. Don't over apply rhyming dictionaries though: they can make lyrics dull and bland. Also, re-wording lines so you're not backed into corner on the next line and forced to use an obvious rhyme can help.
Sometimes if I find myself with writers block when it comes to writing a second verse, but I have a first verse I'm really happy with. In this case, repeating all or part of the first verse can work as an alternative to adding lots of "filler" material in the second verse. It can be better to repeat a line you care about, rather than come up with a new one that's empty of meaning.
Speaking of empty of meaning...
6. In praise of nonsense lyricsNonsense lyrics are when words are used to create a vibe in the song. Neil Fallon from Clutch is excellent at this. T-Rex frontman Marc Bolan also, built a career on nonsense lyrics. This can involve word association, a play-on-words, or just a word or phrase you think sounds cool. When listening to lyrics, people respond to them as emotional triggers. Nonsense lyrics can play on this. Metal bands often use hyperbole to make lyrics sound intense; this can be to the degree that the original subject matter is obscured (Meshuggah are a good example). Obscured meanings are fine in songwriting because the audience project their own emotions on to it. Nonsense lyrics can be creatively liberating, can add originality and quirk to your songs, and can help you write better generally.
7. Non-rhyming lyrics - use sparingly!This is a bit controversial, but I think there's an attitude in some circles that using lots of lyrics that don't rhyme is somehow artistic and profound: I disagree with this. It's often used a crutch for bad songwriting. When used sparingly a non-rhyming line can be used to jolt the listener's attention. This can be good if you have a line you really want to use. But overuse of non-rhyming lyrics makes a song sound jarring, meandering and aimless.
If you can't think of a rhyme, there are several things you can try. Half-rhymes can work really well, words that sound phonetically similar can work too. This is because as you sing, you tend to vowelize words, making consonants less important. Also, your accent and the way you pronounce words changes whether and what rhymes work. There's a video on YouTube where Eminem talks about words that rhyme with orange that exemplifies this point. Learning to write rhyming lyrics is a very important part of songwriting. You'll be rubbish at it at first, but will get better if you keep trying. You'll become better able to express yourself through songwriting. Using rhyming as a creative outlet in of itself adds an extra dimension to your songs.