How should I go about getting bones? I only use them for bonemeal for my crops. I'm terrible at fighting the skeletons and almost always die! How can I kill them without dying myself?
I have a simple solution - find a cave, and find a skeleton spawner. Seal the room (usually spawners are in small, square rooms) from the outside with glass, so that you can see in, and have two vertical blocks of cobblestone so that you can easily destroy them and collect the bones, then get out and put them back. Do not use a door - skeletons can shoot arrows through them. Then, go in through the cobblestone 'door' and destroy the blocks that make up the ceiling, until sunlight reaches every square of the room. Then go and collect lots of oak wood, and make oak planks, then make lots of trapdoors. Place the trapdoors in every square of the ceiling. Now, go out of the room and put the cobblestone back in place, then put the difficulty up. The trapdoors will limit the amount of light getting in. Wait until there are a few skeletons, then go out of the cave, or to the cave if you did not stay, and open the trapdoors from above. The skeletons should die. Then, go into the cave then into then room through the cobblestone - do not jump from above, as you may lose health and if the spawner is very deep down, you may die. Collect the bones, arrows and feathers and repeat the process! At night, make sure that you are on peaceful mode, as this is supposed to be a way of not having to fight creepers.
Bones are one thing, but the use for them is another: Bones for training dogs, or bonemeal, for any number of purposes. There are lots of different ways to gain bonemeal in Minecraft these days; the main constriction of how to obtain it dependent on the version of the game you are playing.
If you are wanting to obtain bones specifically, the other answers cover all those bases: either as [loot from chests (jungle temples, mineshaft loot, Desert temples, etc), from fishing, or from fighting the skeletons themselves. Again, that can depend on how you fight them though: you can just wander around at night, or you can potentially set up a farm which can greatly increase your yield while also removing the danger.
If you are wanting to obtain bones for bonemeal however, well good news! You don't need the bones for that anymore! Bonemeal can now be obtained through either composters, or by looking for fossils[1,2]. Fossils are made up of bone blocks, and bone Blocks are made up of 9 bonemeal.
Alternatively, you can use composters with any kind of grass, tree (leaves or sapling) flowers, or crops. And now they have added Moss, you'll be absolutely swimming in the stuff!
When you use bonemeal on Moss, it will spread out and turn other surrounding blocks into moss as well. By making a stone generator to create a platform, then using bonemeal on a nearby moss block, then breaking the moss and putting it through a composter, soon you won't know what to do with the stuff!
Go mining and get some diamond or iron ore and make some armour. Then make a sword and enchant it. Enchant your armor as well if possible (preferably with books to get projectile protection). Then you can easily kill skeletons without taking too much damage. There is no other way of obtaining bones except possibly in dungeon chests, but if your going to go dungeon hunting, you may as well go mining for some ores, and you will also encounter allot of skeletons.