As the owner of long-haired, double-coated, high-shedding dogs... wearing fur, albeit unwillingly

, is an inescapeable part of my life.
As KF and Sagitta say, first line of defense is regular grooming. Make sure your pet enjoys the activity; go slowly at first, rewarding your pet often.
Second line of defense: Brush your clothing/bed linen/anything going into the laundry with a lint/pet hair removing brush or roller before it goes in the wash. If necessary, vacuum the items with an upholstery brush.
I've tried all those gadgets that are supposed to catch pet hair during the wash cycle. Waste of money; didn't do a thing. But then, sheltie fur was probably the inspiration for velcro.
Third line of defense - thoroughly clean the washing machine, including the filter. With the machines I've had here, normally one only needs to do this infrequently - but if you have shedding pets, you will likely need to do it often - and certainly before the machine 'complains'. (Mine has a compartment that pops open when clogged, meaning you can't do any more washing. You then need to drain the area, take out the filter and clean it.)
If you don't know how to do this, ask the landlord/concierge.
Same goes for the dryer - clean the filter after every use as normal, but also look down into the filter compartment - there is often lint/fur collecting down there. You might need to vacuum it out. If you have a condenser dryer, clean that after every use.
And lastly... be prepared for the toll pet fur takes on a machine. I usually only get 3-4 years out of a washer, about the same for a dryer - and these are machines that are expected to last 10 years plus. I don't know what your liability might be as a renter, but just keep this in mind.
Yes, pet hair is annoying. But a small price to pay for the joy the little critters bring into our lives.