Can someone please share how I can make those cherry blossom branches stick out the cake like that? Would I need to use wires? 

Yup, you would need to use thin floral wire and the wrap everything with brown floral tape.

Yes these are definitely wired.  If you did not care whether or not they stood out from the cake, you could pipe them.

Thanks for the replies! I have size 20 gauge wires. Would that work for that? Yes I’ll probably do some piping too:)

Yes, 20 gauge wires would be more than sufficient to support those small blossoms.  If you ever find that your wire is not strong enough and you don't have a heavier gauge, double or triple it.  Just tape it together.  Just be sure and not stick the wires directly into the cake.

Awesome! Thanks so much for the great advice:)

You are very welcome, dream_cakes15!