Alliterative verse is a form of English poetry that was used to write Beowulf and other Old English poems, but was almost totally abandoned after Chaucer. In my opinion, it's easier to write than rhyming poetry, and has the lure of being ancient.
Lines of English poetry have a beat. Consider Hickory, Dickory, Dock:
Hickory, dickory, dock,
The mouse ran up the clock;
The clock struck one,
And down he run,
Hickory, dickory, dock.
The first, second, and final line have three beats. The third and fourth lines have two beats. The simplest English poems count the beats in a line, and nothing else. More advanced metrical poems may also count syllables, or expect the beats and syllables to be arranged in particular patterns, like Shakespeare's iambic pentameter.
Alliterative verse is a relatively simple form, so we'll only be worried about the beats in a line. Each line should have four beats, just like Star Light, Star Bright:
Star light, star bright,
First star I see tonight,
I wish I may, I wish I might
Have the wish I wish tonight.
Every four-beat line can be blockquoteided into two half-lines with two beats each. When we write alliterative verse, we build the poem out of two-beat half-lines, stiching them together to make full lines, and lines together to make poems. For instance, we could combine the half-line Johnny was walking with the half-line down by the bayou to make a full, four-beat line:
Johnny was walking | down by the bayou.
That's how we make our lines. Now to decorate them. Alliterative verse doesn't rhyme; the main decoration comes from the alliteration.
Alliteration is when the primary beats of two words start with the same sound. A few words that alliterate on the "M" sound: mouse, maker, massive, mumble. It's tempting to think of alliteration as happening when words start with the same letter, but that's not it. Take the word amazing. The emphasis is on the second syllable, which starts with "M," not the first one that starts with "A," so amazing alliterates with the other "M" words: "A massive amazing mumbling mouse meddles with medic's murmuring mango." Hear how amazing fits right in with the other words? That's alliteration.
So, now we have a basic line, four beats, and a basic decoration, alliteration. How do we combine them?
To write alliterative verse, at least one of the beats in the first half-line must alliterate with one of the beats in the second half-line. Taking the "mumbling mouse" example, we could arrange it like this into two lines of poetry:
A massive, amazing | mumbling mouse
meddles with medic's | murmuring mango.
In that example, all four beats in each line alliterate on the "M" sound. It's a neat sound, but if every single beat of every line alliterates, it starts to sound obnoxious. Let's tone it down a little:
A massive, terrible | mumbling rat
meddles with doctor's | murmuring apple.
Better! Ancient alliterative verse almost never alliterates on the last syllable of the line, so we changed those words. And two alliterating beats per line is enough, even through a lot of lines do have three.
Of course, both lines are still alliterating on the same sound. Ideally, you want to change it up from line to line. Let's try this:
A massive, terrible | mumbling rat
bites the doctor's | bitter apple.
There we go. Now each line is alliterative, but on a different sound. That's the basic form of alliterative verse. It's easy and fun to write. Go give it a shot!