call up the network with your old phone and get a pac code and call up the new network and say you want to do a sim swap and give them the pac code, it takes 7 to 10 days.
If your just staying on the same network call up and say you want to migrate your number onto your new sim, this takes 2-7 days.
Make sure you have both sim numbers and mobile numbers to quote as they will ask for them.
Oh save everything on you r old sim somewhere because it will get deleted on the way other, it will only take your number (and your credit if you have a pre pay phone).
Hope that helps :-