We use this blanket I made Chase for Christmas for part of our morning lessons. He's jumped right onto the routine of sitting down on it once it is laid out and waiting for a special toy or puzzle to be brought to him. It buys me a few minutes to cuddle alone with Andrew reading or load the dishwasher without little hands grabbing.
Teaching your toddlers to sit on a blanket and play is very simple. All it took was me sitting with him the first few times, bringing out a toy that was saved for blanket time and then after a few minutes getting up and asking him to sit for a few minutes and play. If he got up, I'd gently set him back down again and bring his attention back to the toy. I'm always within his sight and so even my mama's boy goes for this for five minutes or so.