[Archonsod]

How do you slaughter animals?

You need a butcher & butcher's shop. Then assign a "butcher animal" task the same way you assign tasks to any other workshop. The butcher will go off and slaughter one of the animals. You can slaughter any non-pets (that is, any animal which doesn't have a living owner).

Also, is there a way to train cats and dogs for some fighting?

Build a kennel, then have a dwarf on train animal orders (through the assign labour commands).

I've struck some copper though, so I could make some low quality weapons to last until I find something better.

Your craftsdwarf can make obsidian shortswords, which are damn effective.