As you are boarding, stand directly in front of the train/tram doors as people are waiting to get off. Ignore signs that say you should allow people to exit before you get on. Get huffy when people trying to exit get in your way. Fail to acknowledge the logic that people leaving the train will make room for you if they get off first. Be anxious about getting a seat, forget all this, and race on.
Find a seat of two and sit in the aisle seat. Put your bag on the empty seat next to you, even if it's peak hour. Personal space is too important for courtesy. Or if you can, sit in an aisle seat of four. Put your legs out and look directly at the people sitting across from you. Glare. Question why they are intruding upon your comfortable moving paradise.
During peak hour, crowd around the doors instead of moving down the aisle. No need to disperse amongst the rest of the space where there are more things to hold onto. No need.
Conversely, if there is only one person in the carriage, seek them out and sit next to them. Nobody wants to be alone. If possible, make sure you can face them. For extra effect, if you are a guy, open your legs really wide and be uncomfortably 'there'.
Be a crazy person. Yell at fellow commuters about their appearance. Be really drunk and maybe smelly and hover really closely to people. Ask them for money. Bring an impending sense of guilt throughout the carriage as you whimper "excuse me" to people minding their own business. Maybe have a cigarette on you for full effect.
Listen to your ipod really loudly. Invite everybody into your little techno world of joy. When the tinny beats from your headphones aren't enough, play music off your phone. There's a reason T-Pain rhymes with train. And why else do phones have speakers if not to share the joy of your music taste with everybody else on public transport?
Don't help old people on or off the train/tram. Shouldn't they be taking the bus? What are they doing in the city? Shouldn't they have a license to take public transport? Pretend to be far away, immersed in your music or your book, when a doddery old man gets on the train, so you don't have to give your seat to him, even though you're sitting in one of the seats with the sign marked 'give to people with special needs'.
Take a phone call. Talk really loudly to the person on the other end. Probably have your phone on loudspeaker because the train/tram is noisy. Your life is interesting enough to have both sides of a conversation broadcast loudly throughout it.
The final way to be annoying on public transport is to openly support a football team by attending their games on the weekend. Crowd onto the train talking loudly about how 'we' did in loud, outer-suburban accents, block-coloured breast to block-coloured breast. Permeate the train with uncompromising consistency, an unfortunate surprise to those who take the train for non-athletic reasons on weekends.