I work pretty hard to keep my crochet lint/hair free. Despite this photo, I try NEVER to put yarn on carpet or on the couch or other soft surface. I try to keep the yarn always in plastic bags, even while I'm using it. When I set the project down, I try to set it on a table or back in a plastic bag instead of on the couch. If I set the item down on a table, I try to set my papers/instructions on top of the item so that 1. the cat won't sit on it, and 2. to protect it from lint/dust.
I am grateful (again) that I'm not a smoker. I know that editors don't want a stack of smoke-filled swatches in their offices/on their desks.
If I do manage to crochet a hair into my work, I pull it out immediately and gently. If it won't pull out, I take out the stitches until I can pull it out. I pick off stray cat hairs, and if the fabric is sturdy enough, I take a lint brush or roller to it when I'm done. I will often keep a clean pillowcase on my lap and put the crochet project on top of it, because, guaranteed, the cat has managed to sit on my lap at some point. If the cat has been giving me "hugs", I'll go change my shirt before going back to crochet.
If I am assembling something that has to be laid out, I make sure and close that door to the room it's in so the cat can't get in. Also, I'll lay down a clean flat sheet first, then put my squares down, then if I have to stop, I can fold the whole thing over like a Calzone to keep it clean and in place. If I'm worried about losing the placement of the squares, I'll take a digital photo of it first, so that I have a guide to help me re-position all the elements when I return.
Probably the best thing to do is to never let the yarn ball/skein ever touch the carpet or couch. I also don't pull too much from the skein as I work. I don't want it to "puddle" on the floor while I use it. If I have to frog a bunch, I pull the yarn off the project, letting it "puddle" or pile loosely in a plastic bag, so that again, it is not touching soft surfaces.
PS, don't ever leave a pet unattended near plastic bags. I have had friends who have lost their pets this way. Rest assured, I shoo-ed Charlie out of this bag as soon as I took his picture.