The start of the Alaska Highway is at Dawson Creek, BC. There are all kinds of ways to get there, but once at Dawson Creek, there are only two ways to get to the main portion of Alaska: 1) The Alaska Highway all the way to it's official end at Delta Junction (from Delta Junction to Fairbanks, you'll be traveling on the Richardson Highway), or 2) At Whitehorse, YK, go north on the Klondike Highway to Dawson City, cross the Yukon River on the free ferry, travel the Top of the World Highway to the Yukon/Alaska border, the Taylor Higway from that point, through Chicken and back to the Alaska Highway at Tetlin Junction east of Tok, AK.
An alternative way of getting to Alaska other than starting at Dawson Creek, is to travel the Cassiar Highway from Kitwanga, BC to its junction with the Alaska Highway just west of Watson Lake, YK. No matter which way you go, you'll be on the Alaska Higway at least part of the time...there are only two land border crossing from Canada into the main part of Alaska: 1) The one at the Yukon/Alaska border on the Alaska Highway, and 2) The one at the Yukon/Alaska border at the Top of the World Highway west of Dawson City, YK.
I do hope you're planning on doing more exploring of Alaska other than just Fairbanks! As someone else stated, get a copy of the Milepost before leaving on your trip (the new ones are published and made available in March of each year). In addition to the Milepost, I also highly recommend Mike and Terri Church's book,
Traveler's Guide to Alaskan Camping. And, if you plan on taking any tours, I'd also recommend buying
The Great Alaskan Tour Saver which has many two-for-one tour coupons...taking one tour can save you the price of the coupon booklet (assuming you're traveling with another person...which you didn't state...if you're traveling alone, don't bother with the coupon booklet).