When you select first from neutral, engage your clutch fully, drop the revs right off, the tap down on the gear pedal. This will cause the green Neutral light to go off. Once your moving nicely, roll back the revs, engage the clutch, then tap the gear pedal up firmly, this takes you through the neutral shift and into second.
If you have the revs too high, or the clutch isn't fully engaged, it may slip back into neutral at this stage. If this happens (as frequently happened on one of my old Suzi's), you need to clutch again and tap it firmly up till the green light goes out.
Once you're happily buzzing along in second, the rest of the gears are upward taps till you get into top gear.
On the way back down through the box, your revs need to be slightly higher on the gear change, this is because your engine is turning over at a faster rate than the road speed is allowing for, so you'll hear the revs increase as you go down through the box.
So, from top, engage the clutch but keep your revs slightly rolled on, you'll hear the engine begin to race a little. Now change down one gear (tap down) and GENTLY release the clutch. Over time you will "tune in" to the engine revs, and be able to perfectly match the tone of your rolled on revs to the lower gear - and boy does it feel good when you get it right!
Practice this down shift technique every time you go out, and eventually your gear change will be seamless and smooth, causing no damage to the clutch or chain, and your pillion will love you forever.
Once you've got this one mastered, have a go at block changes - this is tapping through two or more gears when coming to a halt from speed, whilst the bike is still in motion.. real advanced stuff now.