Sharing Notes on the iPhone might be a bit tricky if you didn't do this before.
Step 1. Open your note and tap "Share" button.
Step 2. You need to select "Collaborate" sharing mode. After you do that "Invite with Link" icon will appear. Tap on it.
Step 3. You will see a sharing dialogue. Type email/phone number of the person with whom you want to share the link. Press "Share Link".
Step 4. After you pressed "Share Link" the link itself will been your clipboard. Go to any application and do "Paste" on any text field.