Fine-motor skills can begin very simply, with counting on the fingers or learning finger spelling (see Resources). For strength training, keep a rubber band handy and stretch it between the fingers of one or both hands. Even twiddling your thumbs amounts to a fine-motor activity.
If you always liked embroidery but can't manage fine crewel work now, start with laced leather items, latch-hooked or punch-needle rug-making, or large-scale macrame. If your art was pen-and-ink drawing, try watercolor and explore your abstract side, or take up Chinese calligraphy.
Start with the easier items in folded-paper origami and work up to something more impressive and challenging. Fine use of scissors is harder than it looks, so save it for an addition to simple folding. Take up sculpture, starting with soft modeling clays and putties.
Shoot marbles in a ring on the floor or into a box on a table. You might also build an extended and elaborate trail of dominoes that you and a child can have fun knocking down. Don't be afraid to discover or rediscover building toys, especially if you can share them with a child you love. It's the snapping together that works for your fine-motor skills, though, so don't get hung up on achieving an adult-looking final product.