I've made this run before, so here's the lines you'll need.
Take the Blue Line towards Downtown/Gresham.
Get off at either Pioneer Courthouse Square or the Rose Quarter. Either way, there's a Yellow Line you can board nearby.
Take the Yellow Line towards Expo Center.
Get off at Delta Park/Vanport. Down the nearby steps is a C-Tran stop.
Get onto the #4 and ride it into Vancouver. Get off at the very first bus stop in Washington. If you did so, you'll be getting off onto Broadway between 6th and 7th Streets.
Walk South to 6th Street and take a right (West) for three blocks. You'll be at Columbia Street, which you'll need to cross in order to reach the Hilton (on the left) and Esther Short Park (right).
Regarding the ticket, if you get the Tri-Met All-Zone, you'll be fine. If you don't, you can pay $1.60 on the bus. Note: Right now, this fare is $1.55, but it's looking as if the rate will go up on September 1.
In terms of going back via this system, you can get a express to Portland pass, which is $3.25 right now, or a day pass that's express to Portland, which is currently $6.50.