I'm wondering if in the Lord of the Rings (and others of J. R. R. Tolkien's works) the differences between elves and half-elves were clear enough that an elf meeting an half-elf would be immediately aware of their origins, and vice-versa. From what I understand, half-elves looked pretty much like regular elves, but perhaps elves have some sort of sixth-sense in this matter?
However, those of Elven blood are obvious to Elves, at least going by the one example we have, that of Prince Imrahil of Dol Amroth:
At length they came to the Prince Imrahil, and Legolas looked at him and bowed low; for he saw that here indeed was one who had elven-blood in his veins. 'Hail, lord!' he said. 'It is long since the people of Nimrodel left the woodlands of Lórien, and yet still one may see that not all sailed from Amroth's haven west over water.'
(Return of the King, The Last Debate)
It is not known how Legolas was able to tell this.
Half Elves look like humans to elves and like elves to humans. Males are able to grow beards, which is something elves are unable to do.