The only rule one needs to follow writing a song is a thing known as "listening to your heart". On the one hand it's totally understandable and doesn't need any explanations and if you get it you don't need to go on reading, but on the other - this doesn't tell anything about the spoken process. So I will try to avoid such a vague and mixed definitions and phrases, posting real working recommendations, that could be developed and used in practice later.
1. Don't get obsessed by rhymes and rhythm. They are not the most important issues of the song. You do not need to think about the rhyme at all - it's not a poem. Also some words or strings can be sung faster or slower, you can start singing a single string before a bar, with the bar or even after the first notes of the bar, and of course some notes can be 'swallowed' while some others - stretched. The one and only aim here is to make your lyrics convey your thoughts, feelings, dreams, appeals and so on.
My heart is still yearning
While there's nowhere to go
And now standing next in line
I'm looking at the gates of hell2. Change word order. Songwriting is a kind of art, where standard linguistic rules (grammar, word order, spelling etc.) are not very strict and gives you an opportunity to close eyes on them. Therefore you can easily make your own corrections of sentences or separate phrases, which wouldn't have been allowed anywhere else. Moreover some words like articles can be thrown away and a lot of others can be shortened if there's a need.
To the universe unknown departed their ship
But no friends o' mine on that ship still live3. Search for synonyms and metaphors. Substitute separate words or word combinations with their synonyms or phrases similar by sense. Also use different kinds of metaphors (epithets, comparisons, exaggerations etc.) - just use your imagination. That will make your songs more picturesque, attractable and less standard in used words. Create a song with its own beauty, its soul, create a new world and the more this world will be variable and unconventional (offbeat) the more it will be interesting and enigmatic for listeners.
Enchanted by a blue ribbon of dancing stream
A beautiful creature of light follows the sun-beam4. Write down your ideas. Everywhere at any time remember or write down your good ideas, thoughts or some evanescent emotions and feelings and when you have a great number of incoherent phrases in your note-book you will be able to use them as parts of your new songs.
...home is a place where heart beats in the rhythm of love...
...and what if sun haven't ever existed? Then we would not have known what day is and what night is too...
...people always think just about themselves...
...only drunken one can't see the whole difficulty of the situation...
Well, of course there are a lot of other pieces of advice that can be given, but mentioned ones are the most important and useful, as they were many times checked in practice. Hope these tips will help you.