Especially for felting blankets, it's really quite easy. Basically you have to have 100% wool (or alpaca, angora, etc.) that isn't superwash. You knit up your item. It's best to not use a really tight gauge, because what you want is for the fibers to rub together a lot when you toss it in the wash.
You put the finished item in the laundry, with hot water (and a cold rinse, if possible) and maybe a pair of jeans or some tennis balls for extra agitation. As the yarn gets agitated, the fibers kind of migrate into each other, and because of the rough outer surface on each hair, they get stuck that way.
If you are doing something that is sized (like a felted hat or slippers), you have to keep a closer eye on it, but for making felted blankets for animals, just keep in mind that as the fibers get interlocked, they pull closer together, so you have to knit your object somewhat bigger than you want its finished size to be.
For cat-sized blankets, you might experiment with this by going to a thrift shop and buying a 100% wool sweater (one that says dry clean only) and throwing it in the wash. When its felted, you can cut it into cat blankets or just donate it as is!
recent FOs: Shedir cap, Bricks of Atlantis, Pirates Hat, Citrine Socklets, Teddy bears, 1 entrelac sock
OTN: scraps blanket, Shedir for Teenie, Ice Serpent Hat
NIL: Qiviuk tam re-visited; weatherproof gloves; sweaters
My knitting blog: http://emilai333.wordpress.com/