I actually find coasting in the corners helps me put more power behind my crossovers when I'm coming out (by coasting I mean sexy skating, so I'm throwing my weight into the coast and recovering for a big acceleration out of the corner). I'm a massive diamonder, though, so I crossover into the outside points of the straights. I also find that if I'm sexy skating on the corners this helps me to sneak past on the inside line, sometimes with a little hop.
Push with your crossovers. If you don't get this, try skating along and pushing your left leg behind your right. That is where the power in your crossovers comes from - and it's also why getting low helps. I find if I'm lower I get more power from that push.
Don't skate wide to avoid people. I was so polite when I first started, but, realistically, if someone's going to fall simply because you pass them, they've still a way to go before they'll get 25-in-5 anyway and they need to be able to be passed without falling.
Relax and keep breathing. Don't concentrate so hard you stop breathing.
Hydrate earlier in the day, or the day before. Again, this is probably obvious but skating as fast as you can for five minutes is hellish if you're dehydrated and afterwards you're likely to feel pukey if you gulp down water. Likewise, make sure you have a proper breakfast, not a 500ml can of Irn Bru on the bus.
Get dumped horribly and unexpectedly. I don't necessarily mean literally, but find *something* that gives you that impetus. For me, it was getting dumped, passing my laps the same day was basically a big affirmation that I was awesome and my ex was a poo.
