What is the normal post-op care for a venipuncture site?

Cleanliness. Keep it clean and it necessary cover with a bandaid.
Usually nothing. The site is small and holding pressure for a few minutes is all that is required. Raising the arm may help some. Many will place a bandaid or small dressing to keep any ooze off clothes or surroundings a site for blood donation may be a bit larger and require longer pressure or occasionally a brief pressure dressing. Veins are low pressure.