Many songwriters get by without knowing anything about musical theory. Knowing music theory isn't a requirement for writing great songs. Musical knowledge is, however, an added benefit when it comes to constructing songs. An understanding of the basics of chord progression, writing within key signatures, and how to notate music will make a good background. You can pick up a basic music theory book at a local bookstore or even find basic music tutorials online free of charge (see resources).
There is no set way to structure a song. Over time, the structure of many of the world's hottest hits have demonstrated basic principles of structure that have been successful, but writing a good song is still a matter of hearing what sounds good and being able to turn that into something that people will want to hear. Many rock songs feature a structure that relies on the alternation between verse and chorus, often with a bridge thrown in. Just about any rock song you listen to works on the verse chorus principle, though many don't necessarily have a bridge. If you are just starting out, try writing to a verse-verse-chorus-verse-chorus structure.
Different songwriters have varying writing habits and methods. You might write lyrics on a legal pad and jot chords in over the lyrics where the changes happen, or you might want to notate the musical parts individually, in traditional musical notation. Ask yourself what your song is about, then write lyrics that fit the theme. Don't worry about rhyming. This isn't poetry. While some lyrics might have a rhyme scheme, it certainly isn't necessary. Just think of the verse as the setup of the song. Use the verses to set the scene or define the story within the song. The chorus is the portion of the song that will be sung pretty much the same way throughout. It will have a different musical feel than the verses and should be something catchy and singable. A chorus can be something as simple as the repeated line in "Knockin' on Heaven's Door" by Bob Dylan, where the line "Knock, knock, knockin' on Heaven's door" is repeated over and over again.
It doesn't matter if you compose on guitar, piano, or another instrument. You can simply write down chord changes or you can fully notate your songs. What matters is that you write something that sounds good to you. If you write the song you want to hear, chances are good others will as well. Think about the lyrics of the song before you write your music, if you've already written them. What do the lyrics say and what style of music will fit? You will want to decide if you're writing a ballad or an all-out rocker. Maybe you want to go with a folky or country and western feel. Strum some chords and listen to the way they progress. Try singing your lyrics over what you play. Listen for ways you can use techniques such as going up an octave for a bridge or the final chorus to beef your song up musically. Try changing the tempo for certain sections to see if it adds anything to the song. You might even try playing what you thought was an uptempo rocker as a soft ballad or with a blues feel. With songwriting, get creative and find what fits the song best.