This is the ultimate newborn carry! Three passes over baby give lots of support and snuggles. This is the same basic carry that most people use with a stretchy wrap like the Moby or Boba wrap. This tutorial is with a long size 4, but would probably be most comfortable with a size 5 or 6.
Front Wrap Cross-Carry (FWCC)
This isn't a carry I use often, but others swear by it for babies who are wiggly, pop their secure seat, or who are leg-straighteners. This demo is with a size 3 wrap, but it can also be done with a size 2.