Bus:From Canakkale
Several bus companies (Kamil Koc, Truva) will get you to Canakkale's rather seedy bus station. From there a middle size bus, leaving 7 or 8 times a day, will do the pleasant, 2 hour run down to Ayvicik. This journey takes you past the exit for Troy so you might consider breaking a journey here. If it's early morning, which it may be coming from any distance, the more adventurous can get to Troy on foot and roam the hillside before the tours arive. You can always get back and pick up one of the later buses to continue your journey.
From Ayvicik, which has little to keep you hanging around, it's about 20km to Assos. The minibuses will leave when they're full so you might consider a taxi. Hitching is possible if there aren't too many of you and even the package tour buses have been known to pick up a smiling foreigner. I guess one or two more make no odds.
As usual on these small trips costs should be minimal as long as you make sure that you're paying the same as everybody else.

Leaving Assos in this direction you're pretty much at the whim of the Ayvicik minibus drivers, as most people have done their sightseeing tour by mid afternoon it can be a little tricky if you have a connection to make. Sometimes you can feel that the place just doesnt want to let you go.

From Izmir:
Same story really. Izmir's larger and shinier bus station offers several ways of getting to Canakkale or, more conveniently, Ayvicik and from there you can take to the small buses.

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