By multi-city tool, they mean creating an itinerary with multiple stops. I'd post a screen shot but flyertalk photo loader doesn't work when I'm on my work laptop.

Go to Alaskaair.com and on the main page in the grey square where you can input your search criteria, there should be a link for "All Search Options"

On the page you land at, you can now do a Round Trip, One Way, or Multi-City search.

Click the radio button for Multi-City, then you could search for example:

Flight #1 : NYC (All Airports) to SFO on Friday June 21st
Flight #2 : SFO to HNL on Saturday June 22nd
Flight #3 : HNL to NYC (All Airports) on Sunday June 30th

You can get creative with long layovers, or create more stops... and as long as the fare is all AS, you can use your companion pass to add a 2nd.