East towards Montréal
From downtown, take the number 86 OC Transpo bus towards Elmvale and get off at Southvale / Russell. Keep walking down Russell towards the intersection of Walkley and Russell. Cross the street to the southeast side of the intersection, and go to the shoulder right at the start of the right-turn lane. Wait times from here are generally quite short, taking anywhere from 5 to 30 minutes in most cases. Just make sure your ride is going towards Montreal, as from this point people can be going either northbound or southbound on the 417. Or just walk down to onramp for eastbound 417 there is some traffic and space for drivers to stop on the ramp.
South East towards Cornwall
Cornwall from Ottawa is fairly difficult. It may be just better to just hitchhike to the 401 (follow directions to Toronto), then at the onroutes ask people who are going to Cornwall. (Make sure you get dropped at a onroute going the direction Montreal rather than Toronto, or get dropped at prescott) This is a less direct ride but you have much better chances on the 401.
However, it is possible to hitchhike to Cornwall with a shorter method. Follow instructions hitchhike to Montreal. Tell the driver to drop you at Casselman. take 138 road. This is supposed to be a 80km limit road but drivers treat it like a highway so STAY SAFE.
Take the 96 bus from the Rideau Centre from downtown Ottawa towards Kanata (a lot of buses from within Ottawa will meet up here, but will drop you off on the other side of the mall. Walk through the mall to the Mackenzie King Bridge entrance to catch the 96). You can try getting off at the stop beside the Eagleson Road on ramp for the 417 as it has a good shoulder, or keep going west a little on the bus until it stops at the Terry Fox Centre. Walk up to Terry Fox Drive - there are two on ramps there and one of them has a good shoulder to stand on.
Note: You don't have to go from downtown. Any entrance ramp on 417 will do. Just write Kanata on cardboard.
South towards Toronto
Take the 118 to the furthest West of Baseline. It should be called Baseline and Robertson Rd. Here you will see the 416 highway, which goes as South as Prescott. At the entrance ramp here, you can find a ride usually to Kemptville. That is about halfway. Then on the next onramp get to Prescott. Once at Prescott you can find the onramp for the 401 direction Toronto. Try to get to a OnRoute (Ontario service station). Here there is a lot of restaurants and so people have time to chat with you to determine if they trust you or not. At night these service stations are reliable places to hitchhike. Try to hitchhike at a service station without looking like a hitchhiker, so that you have less chance of getting kicked out.