You can write a verse in many various ways, and you may feel free to experiment with rhyme schemes as much as you want, but for this tutorial I will use a basic scheme that is excellent for the beginning stages of writing but can also be upgraded to more complex versions. The more important thing though, is the thought process behind writing lyrics rather than the mathematics of the scheme. This tutorial may offer nothing new to some of the writers in here, but there may also be a lot of people who can benefit from it. To best show the procedure, I will write a verse in real time. Nothing complex, but just to show you.

So anyway, we start with the opening line which in a way is the most important one, because from there you can expand on it through the techniques which will be presented as follows.
Let's say my opening line is this (remember, this is a line that comes out of nothing):
It's Monday and your brain is about to run out of power
So what you do is you think of words that rhyme with "power" i.e. the ending word of the line which is the main rhyme (multies are a different story, we're keeping this simple). Some of the rhymes that come to mind are: flower, tower, and shower. Now each of this words has a meaning, right? Well you pick the rhyme that you find the most suitable, and you see what its meaning reminds you of. In this case, I'll choose the word "flower". Flower reminds of funerals and giving presents to girls. I'll use the connotation of funerals and basically fill in the line with a meaning that alludes to funerals i.e. someone dying:
It's Monday and your brain is about to run out of power
I'm going to kill you and send your mother some flowers
Other thing I did here, is keep each line a separate statement and of about the same length. This is effective because you keep the content tight and your thoughts are expressed clearly. It also helps with the flow and the breath control.

Next, I advise you to change the ending rhymes on every 2 lines because you'll be able to use a different voice melody to emphasize the end of each line, and it's going to be more interesting if you change the delivery that often. Plus you'll save on rhymes that you haven't used in other verses of yours.
Now, you may use the same rhyme through out the 2 lines and go for some internal rhymes, and/or multies which will make the thing packed with similar sounds but still change often enough. You can also use assonance and alliteration. Like I can continue the verse like this:
It's Monday and your brain is about to run out of power
I'm going to kill you and send your mother some flowers
Slim is a mean man, my team is a machine that goes HAM
I've been ill ever since Sheen drank his first glass of Hen
I did the same thing here with the ending rhymes. Hen, short for Hennessy I believe, rhymed with HAM, and the alcoholic beverage in this case reminded me of Charlie Sheen so that's how I put the line together. I also considered what else rhymed with HAM and Slim so I added more rhymes in between. Again, the content in question is simple, but I'm just explaining the method.

One last thing, you can use the extra rhyming words as a transition for the next line. Like, if my last line ends on Hen, I can use a rhyming word somewhere in the beginning of the next line and proceed to a different ending rhyme. To exemplify:
I've been ill ever since Sheen drank his first glass of Hen
My plan is to scan my PC for a virus, it may be infected
And now I look for a word for infected, and the process can continue so on and so on. The only thing you need to be careful is to try to use the possible rhymes with ideas which would suit the context of the overall song, and if you have a theme in mind, let the rhymes guide you but again, be careful.