With kids like Abbie you use the same strategies that you should be using with other kids - just at a slower pace. So modeling, consistency (ex: not letting Abbie take food from P's plate & then punishing her for doing it at other times), repetition, intermittent positive reinforcement (which others have mentioned), breaking things down into multiple tiny steps, minimizing high stress situations (not taking your autistic kid to Walmart when it's not necessary - focus on going to the doctor, hairdresser, etc). And perhaps most importantly - TEACHING TO SELF-SOOTHE! Kiddo is stressed, having a panic attack or meltdown? Teach them to remove themselves from the situation/signal to you that they need to leave, breathing exercises, distraction (use of a sensory toy, etc).
Now keep in mind that this is coming from a "high functioning" (even though I hate that term, too) autistic mom of a teenage daughter with an adjusted cognitive age of approx. 5 years old. So I'm not in as challenging of a situation as it must be with Abbie.