"Should I just head on up there & start looking & networking?"
The season starts depending on what you're going to be fishing for. Check out the Alaska Department of Fish and Game. It's probably a good place to start your search as they are the ones that make the rules.
"Is it too soon (I'm thinking mid to late April) to head on up, or should I wait til the actual season starts? (I've heard that is very early June)."
You can head up anytime you want to. I myself am going back in 2 weeks driving the Al-Can. If you don't find immediate work with what you want, a lot of the seasonal jobs are starting about now, and there is plenty of other hum-drum work too you could do until you got on a boat.
"Hop on a boat from Seattle? Where would I get off the boat? How much should this boat trip cost me? "
The Ferry will get you from Bellingham, WA to Haines, AK. You can take a vehicle and the driver is free, but you have to pay extra for a cabin (or else you'd be sleeping in the lobby). It's about $750 until the end of April. The summer season the ferry prices about double. (There are other stops along the way as well where you can get on and off) You will have to then either drive, fly, or take another boat to get to Anchorage and from there you can get to the fishing, just depends on where you're going to go. Google for the "Alaska Marine Highway" and you'll find your info there.
"where "there" is "
"There" is proabaly Anchorage, it's the largest city in the state, and you best starting point. I don't know where they do all thier fishing out of, but would probably be on the Kenai Peninsula (Cities such as Seward, Kenai, Homer) or out in the Bering Straight for king crab. Perhaps the Aleutian Chain as well (Dutch Harbor).
Also: You can drive to AK, it's about 50-55 driving hours from SoCal to Anchorage, and the last time I went it took me 6 days.
You can fly, but then you have to get all your junk up there some how (I found the Post Office to be the cheapest a couple years ago)
That's what I've been able to find, and things that I just know from living there. Hope that gives you a good place to start.
-Marisha