Shrimp is usually caught from boats dragging a trawl or net. But recreational anglers have used a standard cast net from shore or one of the local bridges.
The easiest bridge to throw cast a net from is the Daniels (Nags Head Causeway) Bridge. Be warned that there are plenty of debris near the pilings and base of the bridge.
I have caught both green and brown shrimp at various times of the warm months.