Basic glass cutting isn't difficult. It requires 1 cheap tool the courage to try it and like any skill a little practice. But that can be done with almost any broken glass and salvage usable pieces as you practice.
Step 1: Tools
The primary requirement is a carbide wheeled glass cutter. I prefer the type with several wheel on a rotating head, they don't cost any more than the single wheel design and you will damage the cutting wheel at some point(normally by knocking it on to the floor) you simply slacken the central screw and rotate it to the next new wheel. Even so it's still worth protecting the exposed wheel when your not using it.
A marker pen that will draw on glass the finer the point the better.
A ruler to measure and draw your straight lines with. A carpentry square or combination square is a useful addition but not essential.
A straight edged piece of wood to use as a cutting guide,this needs to be longer than the longest cut you are going to make. I'm using an off cut of 2x3/4" (49*15mm) planned board.
Thick leather or Kevlar safety gloves, I don't often mention safety equipment and even here I'm not using it as much as I should.... but broken glass is the sharpest thing known to man. you are about to produce it under your fingers and in close proximity to major arteries. Even with my relaxed attitude to health and safety I'm wearing gloves when it comes to the crunch.
Step 2: Preparation
If your glass isn't new, and if you're reading this I'm guessing you've not cut glass before you ought to practice on some old stuff first, you need to clean it thoroughly.
This is a broken pane of glass from a green house, the cobwebs snails and mud were rubbed off outside a good scrub with wet green scotchbrite with a good amount of washing up liquid will remove any remaining algy snail slim and very importantly grit. If there is paint on the glass scrape it off and scrub it again, either leave it to dry or dry it off with a towel. Note earlier comments regarding sharpness of broken glass take extremely care at the edges.
The surface you will be laying the glass on to mark out and score it needs to be not only firm and flat but also clean and grit free. Even a good cut will produce fine glass particles it is important to clean the surface between cuts as well. A thorough clean up afterwards is also essential these fine shards of glass are a serious hazard.
Step 3: Imperfections
Edge chips and any scratches are a potential source of shattering. This is much more likely if a scratch crosses or is close to the intended cut line. an edge chip needs to be either in the scrap area or away from the cut line
Step 4: Mark It Out
Work out where you are going to cut, mark the longest cut first if you are making more than one cut and mark the scrap area.
Step 5: Set Up and Score
Place your marked glass on your cleaned firm flat surface, place the straight edge on it on the side of the cut line you wish to keep. The cutting wheel is not at the edge of the cutter. Position the straight edge so the cutting wheel will run along the marked line when pressed against the straight edge.
Hold the straight edge down firmly.
Place the cutter at the furthest end of the cut line, press it firmly to the straight edge apply firm downwards pressure to the cutter and draw it towards you along the straight edge. This should be a smooth action with the wheel turning accompanied by a slight crunching sound.
One pass Only is made.
As can be seen my score line isn't perfect however nothing will be achieved trying to redo it
Step 6: The Cut
Place the straight edge on the edge of your table place the glass on top of the straight edge. The scored side needs to remain on top.
The scrap side needs to be over the air, the scored line needs to be as close to the edge as possible but not touching it at any point.
PUT ON YOUR GLOVES!
Apply firm downwards pressure to the good side of the score line spread along as much of its length as you can manage.
With your other hand grip or apply pressure gently to the scrap side. Press as firmly as you can on the good side and then suddenly increase the pressure on the scrap side.
The glass should break cleanly along the score line.
If you weren't holding it the scrap piece has just shattered on the floor.
Step 7: Clean Up
I previously mentioned even a good cut produces fine shards of glass which need cleaning away between cuts. If you're going to let the scrap hit the floor it's best to be working outside on a dirt or grass surface, not in a kitchen as I was, and wear good enclosed shoes or boots and long trousers, flying shards of glass and bare flesh isn't good.
The freshly cut edge has the potential to be very sharp with a fine serrated edge this needs smoothing off. A coarse grind stone of the type used for sharpening a scythe is good for this a smooth piece of concrete or as I'm using the horizontal cement joint in a brick wall do just as well, a gentle rub with little pressure is adequate.