This approach will focus on using handheld glass cutters. Much of what is covered here applies to curves as well, however, I will only focus on cutting straight lines. This is one such cutter:
Image from Amazon.com
The most basic and versatile tool for cutting glass is the glass cutter. There are different styles and features, but all will have a cutting wheel. There are different grips, ones with multiple rotating cutters and many have a ball or similar on the opposite end of the tool (Which is used for tapping the glass)
Prepping your work surface
You should, in general, be cutting glass on a hard surface that is clean of debris. While you might be tempted to cut on carpet or softer surface, this would be counter productive. The pressure you exert with the tool on the glass is the most important factor, so you don't want the glass to move at all unless by your own hand.
The tool, when used properly, will come into contact with this surface so if you have something hard like a metal top, then you might want to put something down like thin cardboard or a self healing mat so as to not damage your cutter prematurely.
Clean glass debris between your breaks. It does not take much to scratch.
Scoring the glass
Glass cutting with hand tools relies on scoring the glass. You are placing a shallow cut/fissure into the glass to guide the eventual break. Getting the perfect score can be difficult to get perfect, but following some basic guidelines, it can be done. If your tool is not self lubricating then you should make sure you lubricate the wheel. This will prevent it from getting locked up with glass shards and binding.
You want the score to be deep enough that it cuts into the glass but not so deep that it starts throwing off chips. The sound the glass is making while your a cutting is important. It should sound like a light zipper and the sound should be continuous from the start to the finish of the cut. Always start and end the score off the glass and avoid hesitation.
Break the glass
Once you have a good score line you should be able to break the glass with ease. These are general approaches
Score away from the edge of the glass: Most cuts you should be able to do with your hand as long as there is room. Place your thumbs close on both sides of the score line. Start applying leverage like you want to bend it in half. Much in the same way you break a chocolate bar.
Score near the edge: If you are having issues getting a hold with your hand then you can use glass pliers or running pliers. Basically pliers with curved jaws with a rubber-like covering to protect the glass. The curved jaws work the glass the same as your hands, using the score line like a fulcrum.
Image from freepatternsforstainedglass.com
Other variations of hand and tool positions exist. It's a matter of applying pressure close to the score line to encourage a break.
If you are having issues getting the break to start you might not have a good score line, the glass might be thick, or you might need to exert more pressure to start the break.
You can use the ball of the cutter to tap near the score line on the other side. Run the ball at the edge of the glass and follow the score line along. You likely can see the glass start to break when it gets easier to see. Once that is done you can come back to hands or pliers and try to break again.
If your score is weak do not try to score on the same line again. It can damage the tool and will create an unpredictable breaking score line. Instead try scoring again on the other side of the glass. While this still could have problems, it is a better 2nd chance approach.
One of several good videos that covers this and similar topic
You can also listen to the sound the glass makes when scoring properly.