The next measure to reduce the likelihood of glass shrapnel is to have a firm control over the amount of pressure that will be produced in the bottle. The easiest way to do this is to make sure that the beer has fermented out, IE: there is no more readily fermentable sugar left in the beer before you add a measured amount of a fermentable sugar prior to bottling. When a beer has fermented out, you will see no foamy krausen on the surface and if you measure the specific gravity with a hydrometer or refractometer the readings will be the same over three days*.
You can add pretty much any fermentable sugar to prime the beer for bottling, the most common choices are dextrose (aka glucose and corn sugar), malt extract and household sugar (sucrose). Sucrose is often viewed as persona non grata - if you will excuse me for anthropomorphising the disaccharide - in the home brew community, and not without good reason. Home brew is still shaking off a reputation acquired, a good few decades back, when sucrose was often used to make up a significant proportion of the fermentable sugars in home brew. The result was often a quite harsh cidery tang to the brew. For the small amount used to prime bottles, this should not make a noticeable impact.
As to the quantity of priming sugar, you can find lots of information on the web to go the full bobble-hat and work out the amount of dissolved CO2 that is likely to be in your beer at its current temperature and possibly even atmospheric pressure or height above see level. Then you can vary the amount of sugar to add, considering this and the level of carbonation you would like for your beer. For the beginner and as a rough rule of thumb, prime at a rate of 5g sucrose per litre of beer. Its best to add this to the beer after first racking it off into another vessel, leaving the sediment behind. If you have got as far as this stage of brewing you will already be aware that everything in contact with the beer must be clean and sanitised and this approach can be applied to the priming sugar by first dissolving it in a small amount of water and boiling it for about 15 minutes. This syrup can then be added to the racked beer and gently stirred in to evenly distribute the priming sugar throughout the beer. In batch priming like this, you should have consistent carbonation in all your bottles.
Next, fill your bottles with the primed beer, leaving an ullage (the head-space between the beer and the bottle top) of about an inch to an inch and a half. This process is made all the more easy by the use of a bottling stick. If you haven't seen one, it fits on the end of a syphon tube or tap on your bottling bucket and releases the flow of beer only when pressed into the bottom of your bottle. This allows you to control the flow of beer easily and with the beer flowing when the stick is in the bottom of the bottle, aeration is reduced. The bottling stick is then lifted once the beer reaches the very top of the bottle and the beer displaced by the stick leaves just the right ullage once the stick is removed.
Here's a video showing a bottle stick in action:
the clear bottle helps the demonstration, but brown glass is preferable to reduce the impact of sunlight on beer. If you do use clear or green glass bottles, then be sure to store them in a dark place.
Once filled, then cap the bottles and store at the same temperature or a little higher than that of the primary fermentation, for at least a couple of weeks. Perhaps a month or so if you can bare to wait for the beer to condition and mature. That said, many home brewers find that some of their brews are best imbibed young, so will crack open a bottle after ten days and assess where to go from there.
Bottling is a comparably affordable way to serve your beer, many home brewers stick with it, but many move on to kegging and force carbonating, more of that later...
*The specific gravity may settle out if you have a stuck fermentation, so if the specific gravity readings are higher than you would expect for a finished beer of that style, then take steps to rouse the yeast back into action to finish the beer, which could include stirring the brew or adding yeast nutrient.