You need to find a dungeon which has a mob spawner inside. (It looks like a little cage with fire and a miniature version of the mob it will spawn.) Mob spawners can spawn in dungeons Zombies, skeletons or Spiders. In abandoned mine shafts they can spawn cave spiders. In strongholds they can spawn silverfish. In Nether Fortresses they can spawn blazes.
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You can't, but you can change it by sleeping in a bed. Your spawn point will be changed to the location near the bed. If the bed is removed, then your previous spawn point will be used.
Also, third party programs can be used to change your spawn point, such as MCEdit or NBTForge (outdated).
You can just go on multiplayer, find a Bukkit server and place down a mob spawner by using the /give command to give it to yourself. Also, if you want to change the mob that spawns do /spawner while looking at the spawner and say what type of mob you want to spawn.Example /spawner creeper to change it into a creeper spawner.
As for actually creating, texturing, and programming a mob in minecraft, go obtain sufficient java knowledge and search up some modding tutorials in the minecraft forums.
you get an egg and right click so then the animal should appear where ever you place it
To spawn mobs by suing commands you need to type in /spawn [name] [quantity]. An example of this would be /spawn wolf 6. You can also span mobs by using spawn eggs.