My 17mth old started with full on tantrums at about this time. I tell him no (which he didn't understand at that point, but he did after a few months), then i physically take him away from whatever it is, or take it off him and put him on the floor away from the cause of the issue. Then I get down to his level and put on my sternest voice, look him in the eye and say, 'No, we don't put toys in the DVD player. Mummy is not happy with you. Do you understand'. He now sticks his bottom lip out and nods very seriously (I have to try soooo hard not to laugh) and then I walk away and leave him yelling for a minute or so.
It normally burns out pretty fast. But full on ones can last 20 mins, I just ignore for as much as possible unless he's becomng dangerous to himself
The tantrums improved a lot as he started to walk and talk, plus he absolutely knows that when i say 'no' I mean it. So a 'no, come away' works about 90% of the time. But we get the occasional corker....
He's very spirited and needs firm handling. I'm sure a lot of people would be horrified how firm and strict I was with him from a very early age, but I'm sure this has paid off as his behaviour is SO different now.
He's my second child, very different from my angelic FB!