Latch hook rugs take a long time to make. The ideal situation with this sort of treasured craft would be protecting it from all dirt and grime, but messes happen--especially if there are kids and pets around. While dry cleaning is the most universal cleaning option recommended by the manufacturers of latch hook rug kits, there are several methods you can try for cleaning a latch hook rug on your own.
Comb as much pet hair out of the rug as possible with a wide-tooth plastic comb--take care not to split the yarn fibers. Or, use your fingers.
Hand wash a latch hook rug made with cotton yarn in cool water. Use a mild liquid laundry soap only if absolutely necessary--test on an inconspicuous section of yarn before washing to make sure it will be color safe.
Understand that while most acrylic latch hooked rugs are safe to machine wash, they'll still last longer and be less likely to become damaged if you wash them by hand. If you do use a machine, stick to a front-loading washer to avoid the damage often caused by top-loaded agitator based models.
Freshen the latch hook rug by adding a half-cup of baking soda or a scoop of Oxy-Clean to the wash; this works whether you're washing it by hand or in a washing machine.