The US tradition is to have a shower for the first baby, before she or he are born. People contribute towards gifts which first time parents are unlikely to have, and generally women (can be mixed) get together and hand over the gifts, eat some cake etc. There's also a strong tradition, of wishing the mum well, giving her any hints about the newborn days etc.
Of course, commercialism has rampaged in, and often there is a gift list at a particular store so people can make sure they get a gift that is wanted and not duplicate. However, it would be considered VERY rude to expect people to contribute - often work colleagues get together and buy things, also, a shower is arranged by friends not by the mum. Every little gift, even a pair of socks, is likely to receive a thank you note/email.
After the baby is born, some flowers or a card might be sent. Good friends will drop round meals, but there won't be a rush of gifts, that just happens once.
UK older tradition is to wait until after the birth (for mainly superstitious reasons) and then send/take a gift.
I keep hearing things on here that imply some people have heard of baby showers, and see it as a gift-fest so focus just on that.