Rights of Way

Port keeps clear of starboard

The green sailor who is on a starboard tack has right of way of the Purple sailor who is on a Port tack.
Purple sailor must keep clear.

If both the green and the purple sailors are on the same tack then the leeward craft (that's the one furthest downwind) has right of way.
The sailor on a broad reach should give way to any windward sailor on a tighter heading.
Purple sailor must keep clear.

Board behind keeps clear of another further ahead.

If the purple sailor approaches from behind the green sailor, who is on the same tack, the purple sailor must keep clear.

Tacking or gybing board keeps clear

The purple sailor who is going to tack must keep a watchful eye on nearby approaching sailors on the same tack who wish to stay on that tack.
The purple sailor keeps clear.

Keep clear of larger/commercial craft

Keep clear of larger vessels, even if you're are on a starboard tack.
Although the 'power gives way to sail' rule applies, it usually makes better sense for sail to keep clear, especially as the larger craft may be navigating a channel or doesn't have enough room or time to manoeuvre.

An easy way to remember which tack you are on is:
if your 'right' hand is nearest the mast it's your 'right' of way.