Alaska.how do you go about............
To amplify on rphelan's comments, if you don't travel in the June to August timeframe, you will find many of the campgrounds along the highway closed. The Milepost comes out every year (this way they get to milk the advertisers more frequently), so try to get the most up-to-date one.
The most spectacular part of the highway is probably Muncho Lake. Consider leaving the highway and going down to Skagway, and then taking the short ferry ride to Haines and back up to the highway. Other highlights include Valdez (mediocre town, great for getting out on the water), the Kenai Peninsula, and around Denali. On the topic of Denali, in summer the mountain is usually shrouded in clouds, but the best view points are to the south. Denali STATE PARK, just south of the national park, is worth some time but often overlooked.
If you feel adventurous, consider driving the Dempster Highway to Inuvik, NWT. It's 450 miles of good gravel road--each way; with one gas station halfway up! You can stop at the top of mountain passes and see no sign of human existence as far as the eye can see. Inuvik has a lot of eskimo residents, so it's kind of cool to visit the local supermarket and be see women cruising around in beaded mukluk fur boots! Also, towards late July/early August they have an eskimo art festival, with artists coming in from the remote villages and even some of the islands in the Arctic Ocean.
The Alaska Highway pavement between Burnaby Landing YT and Tok AK is notoriously bad, due to the permafrost in the soil thawing during the summer, breaking up pavement. Otherwise, the roads are pretty good. Figure you'll probably end up with one or more rock chips in your windshield from this trip. Also consider going one way on the Cassiar Highway, which runs north-south through BC, to avoid retracing too much of your route.
I would suggest leaving a "toad" behind, as parking is plentiful for large rigs. However, if you have some kind of boat and enjoy fishing, you might want to bring it along instead.
Like others have said, getting firearms through Canada can be a real hassle. Declare all your alcohol--duties are surprisingly low, but the penalties for getting caught severe. For example, several years ago we entered the US with something like 10 cases of Canadian beer and several cases of Canadian wine, and the duty was under $10.
Inland and the farther north you go, the more mosquitos become a problem. Many of the campsites up here look rather spartan--more like gravel parking lots than the wooded and secluded campsites you probably covet. There's a reason for this, besides being cheap! Open campsites have more airflow, and thus fewer bugs. In some locations, a wooded campsite in a valley along a stream will be so bug-infested that you'll not want to leave your unit!
Up north you get ridiculous amounts of sunlight in the summer. Thus, inland temperatures are surprisingly warm, even above the Arctic Circle (1000-plus hours of nonstop sunlight can eventually heat things up). Along the coast, the weather is milder and moister. You may want to find ways to really darken the inside of your unit so you can sleep at night. Many people use sheets of a silver foil/bubble wrap insulation cut to size and put it between their windows and blinds at night.
As the season is quite short, some campsites do sell out. Therefore, I would suggest planning an itinerary and making reservations. Most campsites have very liberal cancellation policies. The primarly scheduling chokepoint typically is getting into Denali Park. You have to reserve a spot on a shuttle bus into the park if you want to see anything--you normally aren't allowed to drive very far into the park. Campsites in the NP are your typical hookupless (is that a word?) sites, but there are full service campsites within a few miles of the park entrance. There are only a few campsites in and around Anchorage, but you can overnight in the parking lot of Sams Club or WalMart if you can't find any space. Finally, on the Kenai Peninsula, campsites can be next to impossible to find when the salmon are running or there is a fishing derby going on, so plan accordingly.
In summary, it's a very doable trip, just make sure your equipment is working, and plan your trip well. You can get parts and repairs up here, just remember that everything is expensive, and you'll sometimes have to wait for parts to arrive by air. Plus, I can't think of anything that's cheaper in Canada than the States, especially now that the US dollar exchange rate is so bad.