On the ground there is a shuttle bus that is going up the hill to the entrance of the crypt chapel. From then on, inside, there is escalators to bring you to the upper parts and the main basilica.
As for the access to the Oratory, no problem if you have a car (parking lot available) but if you want to use public transportation do not go to the Côte des Neiges metro station, it is nearby but with no direct link and a tad too far to walk for somebody with hip replacement. Instead take the bus no 51 from the Laurier station, it is a 20 minutes ride but you will go trough picturesque Outremont borough and at the foot of the hill of the Université de Montréal.
Another solution is to take the bus no 166 at the downtown Guy-Concordia station but service is more sporadic and the bus can be very crowded.