For this, you'll need Guitar Pro, or a free equivalent like Tux Guitar. Something that will allow you to develop your ear along with your ideas.
My personal songwriting method is one I find absolutely wonderful for someone who is required to handle multi-instrumental composition, but only plays one or two instruments.
When you're just starting out and your ear and mind aren't entirely in sync, I recommend beginning with a nice, simple 4/4 drum groove. Picture it with the kick on the 1 beat and the snare on the 3 beat, with hi-hat hits on all four.
If your band has a keyboard, this is the time to pick out a sound and bring it in. I recommend a whole note with a simple triad. From here, use the keyboard to dictate the melody. If you don't have a keyboard, do the same thing with guitar chords; open chords, barre chords, power chords; they'll all work.
For instance, a very simple example to illustrate my point thus far is a vi IV V progression on the keyboard, with the iv being a whole note and the IV and V being half notes. It's a very generic progression, and I wouldn't recommend using it in a song unless you want an equally generic sound. However, it'll work for the purposes of this lesson.
At this point, grab your guitar and start riffing along to this basic sound you've established. Coming from my background genre of progressive metal, that usually ends up being something nice and complex on the low B string, but of course, your style may vary.
With the guitar riff plugged in, I'll typically go back and rework the drums just a little bit, considering that the basic beat was quite simplistic. I prefer to add some swing to the hi hats by moving them slightly off-beat, or perhaps sync up the kick drum with the rhythm of the guitar riffs, depending on the level of "chug" I want. The snare is generally best on an accent regardless, so I tend not to move that too frequently.
Returning to the tab editor, I'll add the melody of the vocal line to compliment whatever harmonic content I've established so far, with the vocal line's rhythm dictated by the lyrics.
Then, as a last step, I'll bring in the bass guitar. There are several schools of thought when it comes to composing bass lines. Some people love super-complex lines with a ton of passing tones and arpeggios, a la tech death. In the case of Mute Prophet, however, I tend to favor the approach that the bass follows the melody of the guitar riffs while (fairly strictly) following the rhythm of the drums; bass really needs to lock in with the drums, especially the kick.
The reason for deciding between simple bass lines and complex bass lines does not require too much thought: Quite intuitively, it's just that there's already so much harmonic content in Mute Prophet between the keyboards and our two singers, that it would be redundant and confusing to use the bass as a melodic instrument as well. It's better off adding power to the groove. As always, your philosophy may vary.
And that is how, one section at a time, you can begin to write your music. It's truly not as complicated as many people make it out to be: The only thing that's required is enough practice to train your inner ear and have the knowledge of HOW to get the sounds you want. And that all comes from just doing exactly what I've outlined here. Enjoy!