'll try to expand here - if I'm not answering your questions or am unclear, just let me know.
With the method I use, you can choose to bottle it as sweet or as dry as you want. For my tastes, 1.010 specific gravity is about right, but you can also be guided by your taste buds. I watch the fermentation pretty carefully for a few days, when it appears to be slowing down, i take a hydrometer reading and taste the sample. Depending on the outcome, I may do it again the next day or in a couple of days. It takes about a week for the cider to ferment to the level of dryness/sweetness I like, which is what I would call semi-dry.
Alternatively, you can let it ferment out completely dry, where the yeast eat all the sugars, and then back sweeten it with more juice. Folks who use that method then have to add another chemical to stop the fermentation (because the yeast will start up again, eating the sugar in the newly-added juice). Then they can keg it to get sparkling cider or bottle it as-is for still cider.
I really like sparkling cider, though, and because i generally brew with an eye to using organic ingredients, I like to use the pasteurization method rather than the chemically-induced method, if that makes any sense.
So, at this point you've got a carboy full of cider that has fermented to the point where it is as sweet/dry as you want it - but if you let it go, it would keep on fermenting. The next step is bottling.
I'm unfamiliar with how you bottle wine or mead, so i don't know what equipment you have. I use a bottling bucket with a spigot on it, attach a tube to the spigot with a bottling wand on the end of the tube. I don't think it really matters how you get the cider into the bottles though.
The bottles you use, though, are very important. You cannot use ordinary wine bottles for sparkling cider - they are made for still beverages, not carbonated and are not strong enough. You must use beer bottles or sparkling wine bottles. If you use beer bottles, you would need to get a handheld bottle capper (not very expensive) and caps (very cheap). But sparkling wine bottles with corks and wire are fine too.
With the method I use, we are carbonating in the bottle, so we need yeast and sugar to be present. There is still residual sugar left in the cider, but because I don't want the cider to get any drier than it already is, I add priming sugar - regular cane sugar from the grocery store is fine. The yeast will eat that up and leave the sugar from the juice, and the carbonated cider will have the same balance of dry/sweetness as when i tasted it prior to bottling.
Before bottling, for a 5 gallon batch, I boil 2/3 cup of white sugar in two cups of water. The boiling is to get it fully dissolved and sanitized. I let it cool to room temperature (you can put your pot in an ice bath to speed the process). Then I pour the priming solution into my bottling bucket and rack (via a siphoning tube) the cider into the bottling bucket, onto the priming sugar. I have no idea if i need to be as careful as I am about not oxidizing the cider - not splashing it around. With beer, you need to be careful about that at this point, but i'm not sure about cider.
In any case, i'm careful not splash it - i take the siphon tube and put it down into the priming sugar solution, so that the cider is flowing out and through the solution, not splashing. This also assures that the priming solution is thoroughly mixed into the cider.
Then I bottle and cap. I put the capped bottles in a relatively warm space, low to mid 70s if possible, to help the yeast get active.
After a few days, I put a bottle in the fridge for a few hours and then open it, to check on the carbonation level. Assuming its under carbonated, I wait a few days and try another, until the carbonation seems right. If you use sparkling wine bottles, this method could be pretty wasteful - the bottles are so much bigger than beer bottles.
The risk here, as you noted in your OP, is exploding bottles. So when the carbonation is right, I then pasteurize the bottles in a hot water bath to kill the yeast. I use a large stock pot, with 190 F water - i put about six bottles in at a time and let them sit for ten minutes. I leave a floating thermometer in the water, so i can monitor the temperature and add heat if necessary, before putting in the next set of bottles. I use kitchen tongs to carefully put the bottles into the water bath and take them out.
Hope this is helpful, MW. You might look around the cider forum for the other method I mentioned - ferment dry, back sweeten and stop fermentation with chemicals (sulfites, maybe?) But for me, this pastuerization method fits my needs.
