I didn't really do any expressing at all by hand, I was on the pump from day 1 - but things that were helpful in general -

Heat before you pump - like Surprised said, a warm washer or towel can help a lot with let down.
Being relaxed - still now if I am stressed I get a lot less. If it's not a great time & it's just not happening for you, leave it & try again a bit later.
Keep up the fluids, and rest. Lack of sleep affects supply.
Massage the breast can help, down towards the areola.

Good luck with it