As Josephine can already express herself quite well, I've been really trying to focus on her "explaining to me how she feels" about something instead of lashing out and stamping her foot or so. This helps limit tantrums and also helps her learn how to label different moods/feelings etc. So to nip a tantrum in the bud, I've asked her to rather talk and try to explain to me what she wants, why, etc. When I see she looks cross, I say "Josephine, you probably feel cross now. Please tell me what is making you cross. Talk to me. Don't throw your toy/scream".
Today, we were playing with a little puzzle. I was trying to get her interested in it, so I was purposely putting the pieces in the incorrect places, trying to squeeze circle ends into square points and so on...just for her to say: "No, Mamma, no! Not like that! This piece fits in ...here! Not there! Silly Mamma!" Anyway, at one point I said with a bit of exasperation (just pretending): "Hmmm! This piece just doesn't fit here!" (hoping for her to take it and put it in the right place). Her response was so funny: She looked at me with her head tilted, big eyes. "Ok Mamma. Just talk about how you feel now" (sounding like a little psychologist!) "You feel cross, Mamma? Just keep twying Mamma. I help you. Come on Mamma. You can do it!"