If the missing button was toward the top of your shirt or on your pants, grab a sturdy paperclip, hook it through any thread loops left from the button or the surrounding fabric of the shirt, and then slide it through the button hole!
Just use a twist-tie, like the kind that comes on a loaf of bread, as a makeshift needle and thread.
Yes, you can sew buttons on with a sewing machine. … Any sewing machine with a zig-zag stitch partnered with a button sew-on foot can have a button back in place within minutes. Sewing machine companies have had feet to sew on buttons going back to when a sewing machine could first sew a zig-zag stitch.
It’s reasonable to expect your dry cleaner to replace any missing or broken buttons on your business shirts, free of charge. Many full service dry cleaners have their own onsite sewing and alteration service and will provide complimentary button replacement on shirts, as part of their cleaning service.