Not hard at all. The only thing you need is the right kind of pet.
So goldfish and budgies are right out.
The best pets are the fluffy ones – the ones that grow a decent undercoat in winter. Huskies are good, and so are long-hair cats like Maine Coons. Also, Angora bunnies, and some lionheads, and I wouldn’t be surprised if some guinea pigs and ferrets didn’t produce small, usable amounts of undercoat.
The fluff can be collected through normal grooming. Keep it in a clean, sealable plastic bag until you have enough. When you have about 100g/4oz, you can try removing the hairs from the fluff, wash (if you don’t like spinning “in the grease”) and card, and spin.
This first spinning effort will tell you whether the fluff is worth spinning on its own – some of it may be too short – or whether you’d be better combining it with a longer fibre, like wool or cotton.
Here’s some people who made clothing from their dogs’ hair:
These People Are Wearing Sweaters Made From Their Dog’s Shed Hair
There’s even a company – Knit Your Dog – that will do the hard work for you, if you’re not crafty:
And a woman who works exclusive with dog har, and writes about it:
The main problem with cat hair is there’s comparatively little of it. I’ve only really heard of people felting with cat hair:
Crafting with Cat Hair: Cute to Make with Your Cat
Angora bunnies produce Angora wool, that fluffy, soft stuff that makes gorgeous, expensive sweaters, so that’s pretty mainstream and commercial. However, here’s a video of a woman who keeps Angora rabbits (and poodles), showing the process of producing items from bunny to needle, which would be the same for any other animal fibre: