As an appointed assistant referee, when and how do I report foul play?

Only if the match organiser has authorised assistant referees to signal foul play (Law 6.27a). Then:

1. Signal by holding the flag horizontally, pointing infield at right angles to the touchline (Law 6.27b). World Rugby guidance is to signal every incident of foul play, even if you think the referee saw it.
2. Stay in touch and keep doing all your other duties until the next stoppage (Law 6.27c).
3. Report only when the referee invites you; you may then enter the playing area (Laws 6.23 and 6.27d). Let the referee lead the conversation and give: the player's number and team, what the offence was, and where it happened.
4. If asked, recommend a sanction: admonishment, yellow card or red card. The referee may decide differently.
5. If your verbal report leads to a sending-off, give the referee a written report as soon as possible after the match; the referee passes it to the match organiser (Law 6.27e).

Apply World Rugby's Head Contact Process when assessing head contact.