It’s not hard. basic steps:
1-- build site here using a mirror
2-- when you are ready to switch over, on the 1and1 side change the nameservers to dreamhosts which are
3-- optionally before the next domain renewal you could transfer the domain to dreamhost as far as the registrar goes, or simply leave that alone and renew it at 1and1
Additional infor for #1 above:
Is it a wordpress site your bring over or something else? Are they on a linux or windows server over there?
the more you tell the more specific we can be…